00:00 Hello my name is Oyase Sunday, I'm taking you mathematics the Jss 3 2 class we have an

00:19 interesting topic for you today, that is the whole numbers part 2, I'm not the series 2,

00:26 we looked at the series 1, we looked at factorization and standard form, and our express decimals

00:35 in standard form, all numbers in standard form, now this is the 2 of the all numbers and

00:43 we expected to know that as the basics for the series 2, now what are the objectives

00:50 of the class, the objective is the application of prime factorization, remember we did prime

00:55 factorization before in the series 1, where we had to look at the factors of a given number,

01:02 now we look at the application of that, too we look at find the lowest, the least common

01:09 multiple of numbers, which is probably called LCM, I will find the IS common factors, which

01:16 is called the HCF and identify squares and square root of any given number, they were

01:25 going to find the square root of perfect squares using the factor method, it's a long process

01:31 or two, so let's kick start, yeah, I was talking with the lowest common multiple, it's

01:38 known as the LCM, the lowest common multiple, the LCM, the lowest common multiple is the lowest

01:45 or the smallest all number into which two or more numbers divide without the remainder,

01:53 now once you're going to do that, you have two methods you can apply, when doing the LCM,

01:58 which is the lowest common multiple, two methods, the first method is the prime factorization

02:03 method and the second method is the division method, that the method where you have to apply

02:09 division, now move up, let's pick an example one of that LCM, find the LCM of 22, 30 and

02:19 40, find the LCM of 22, 30 and 40, we're going to be using the two methods, two you could

02:27 have an idea on how you come about, so let's pick the first one, we have example one,

02:34 we're looking for the LCM, pick the first number, 22, what are the factors, the prime factors

02:40 of 22, the method A, we're going to be expressing the prime factors of 22, what are the prime

02:47 factors of 22, they are 2 and they are what, 11, these are the two prime factors, to which

02:55 22 can be divided, remove to the total second one, 30, like I said, in the first series,

03:02 we've had how to come about the prime factors, that's from the series one, so it's an application

03:08 of that knowledge, now we move to 30, what are the prime factors, numbers that can divide

03:13 30 without the remainder, our prime factors, we have two and then we have three and multiply

03:23 by five, so two times three, six, six times five, we give 30, so these are prime factors,

03:29 move to 40, that the prime factors of 40, we have two, multiply by two, that's two times

03:36 two, that's four, times another two, then times five, now these are the prime factors,

03:44 at which you could express your word, your 40, now how do you not pick them out, so looking

03:52 at them, you have two, two is to power three, we have five and we have 11, so what do you

04:03 need to do, pick them out, so I will have my LCM from this, pick it out, my LCM will give

04:12 me two, two, two, two, two, so we have two is to power what, three, multiply by, which

04:19 of the value do I have again, I have three, three is needed, which of the value again do I have

04:25 I have five, then which of the value do I have again, I have 11, so I have, so that gives

04:37 me two is to power three, that's eight, that's eight, that's two times two, ten times three,

04:44 times five, times eleven, that gives my final answer to be three, two, zero, now that's method

04:54 eight, using the prime factorization, four method B, using the division method, what we need

05:01 to do, under the division method, which is method B, the division method involved the use

05:10 of what will affect us the division out, so you pick in the numbers, what are the numbers,

05:17 the numbers are 22, the numbers are 30, and the last one is 40, look two, what prime numbers

05:29 can divide them without remainder, we pick two, two in 22, it's 11, two in 30 is 15, two

05:39 in 40 is 20, now what again other numbers can go, we've started, we move to the next two,

05:48 two cannot go in 11, two can go in 15, but two can go in 20, that's ten, you go again

05:56 with a two, as far as two, until you exhaust two before you move to the next number, two

06:01 can go in 11, it can go in 15, but it can go in 10, that will be five, now we've exhausted

06:09 two, from the division, to move up, again, now what also can go, at this point you look

06:16 at the next number, next prime factor that can go, oh 11, 15, five, we can use three,

06:23 okay, picking next three, three can go in 11, three into 15 would give five, and three

06:30 can go in five, so five comes down, five is a three is exhausted out of the equation,

06:35 so we have what next order can go, four is not, five is yes, five, five can go in 11, five

06:42 can go in five, one, five can go in five, one, last value remaining is what 11, 11, 11,

06:49 11, 11, 11, long division method, following, you don't start with 11, you start with the

06:55 least, then you go to the what, to the highest, now when you move up the scale, you now

07:01 say your LCM, your LCM, you bring out all the values that you have, that will be two multiplied

07:08 by, that is two is two per three, two two is three, and that's two to two multiplied by three,

07:15 multiplied by five, multiplied by 11, which gives us the same answer as one, three, two,

07:21 zero, two drop, so you see, you could use the prime factor, you could use also use the division,

07:29 each of them is more in the clear, I put, you expected to get the same answer, now, let's

07:36 take one, let's take another example for a clarification, so we could have, oh, this is

07:41 LCM, this is each, now we have an LCM of the number, these are the two numbers, just three

07:47 top, two numbers, LCM, so we have example two, or the LCM, we're looking now for the LCM

07:55 of 36, starting from the list, what are the prime factors, method A, my A method, what are

08:01 the prime factors, I have two, multiplied by two, multiplied by three, multiplied by three,

08:08 from the prime factors, list, then I have 48, for the prime factors of 48, I have two, multiplied

08:17 by two, multiplied by three, multiplied by three, multiplied by 11, now pick out the factors,

08:26 you will see you have two, two, two, two, yeah, you have two, two, two, two, three, yeah, you

08:31 have three, three, three, yeah, again, you get it, you have, what do you do, you have, you

08:36 have three, three, three, yeah, again, then you have 11, so the LCM, from your, would give

08:42 us two is to part two, multiplied by three is to part two, and multiplied by 11, so I will

08:50 have two is to part two, that will give us three, nine, six, now what the, what types, if you

08:57 get two, now using the division method, division method method B, also for clarification, let's

09:06 see the division method now, in the division method, that's method B, it will give you, we

09:13 have it as right out the division, what you want to divide, that's 36, and 48, we love, what

09:20 can go, two, start work with the two, so I can start off with the two, two, into 36, that

09:27 gives 18, two into 48, that gives 22, move up again, until you exhaust the power of two,

09:35 two yeah, give us nine, two into 22, that gives 11, you know, now if you look up again, very well,

09:44 can two go in this, no, you start off with three, now, three into nine, that gives us what, three,

09:52 it cannot go in 11, three can still go wrong, three, one, three into 11, cannot go, and the last one

10:01 is 11, one, one, all through the scale, now put it up, my LCM remains LCM, remains two times two,

10:14 times three, times three, times 11, now which gives me my, gives me 396, now looking at the two

10:28 methods that have been applied, that you're going into the division method, or you're going to

10:32 the prime frustration method, you are expected to get the same answer, it becomes, it becomes an easy

10:40 process to go, now, let's go to the next part, which is the HCM, the IS common factor, now the

10:48 IS common factor is the largest O number, remember LCM is the smallest, this is the largest O number

10:55 that divides two O number without a remainder, in the HCM tool you follow to the process of other

11:03 prime factorization or division, but yeah, you'll be picking the highest, not the lowest, so

11:11 picking another example, now, we are saying we should find the, find the world, find the IS common

11:19 factor of 504 and 588 will follow the two methods, so we have example three, on the log, so I have

11:30 followed the division methods, I have 504 and I have 588, now going to the process division method,

11:41 now what's the division method, I could just say O, so in the division method, take notes, take

11:47 note the division method, I will separate it, it could also be in them together, so let me take

11:53 it off, following the division method, you could say O, okay, picking the first one, 504, go, and 588,

12:04 now let's go, from the division method, now, we could separate it, the two, okay, so we have what can go,

12:13 what do we have, what do we have, we have, we have, okay, we have two, two into five, oh that will give us two five,

12:24 two into five, 88 will give us two, nine, four, now, can two, two again, we give us one, two, six,

12:39 two will give us one, four, seven, can two also go again, I've looked to, this process can

12:47 two go, yes, two can stay up, I have two, that gives us, one into one, two, six, that gives us 63,

12:55 can two go into one, four, seven, it cannot, so one, four, seven, comes down,

13:02 so, look up, now what does it can go again, now we're moving to the world of three, two can go,

13:12 into the world of three we have, yes, to be 21, into one, four, seven, we have 49, now, can three go again,

13:21 can three go again, yes, I said three can go, can three go, yes, three, what do we have, three,

13:29 into 21, that gives seven, can it go in 49, no, it cannot, so, continue, what else, three is exhausted,

13:39 move to what, seven, now I can seven go here, one, seven into, that will give seven, one, then

13:47 the final seven, take it as one, one, that when you bring out this, bring them up, bring them up,

13:56 you are expected to have, out the process, so when you bring out the process, I'm supposed to have,

14:01 separate them into the two, so for these two, I have what divides them, I have 222, 223,

14:10 the LCM, so, I have two multiply by two, multiply by two, that's three, two, multiply by three,

14:21 multiply by three, then multiply by seven, that's for the first one, then for five, eight, it's

14:27 the point factor number, I have two multiply by two, two multiply by two, and then multiply by two,

14:40 multiply by three, multiply by seven, multiply by seven, now, draw it up, what will not be the itself,

14:49 the itself is the IS common factor, IS common factor, what are the IS common factors, we have two,

14:56 the common between them, stock it up, two, common between them, two also is common, two times two,

15:04 times what do I begin, three, common between them, and three, then seven again, common between them,

15:13 seven, so that gives us what, 84, so abuse division method, and that is the B method, the A and the B

15:22 method, so with that, we've been able to get how you could use a division method, and how you could

15:30 use the prime factor to get your word, your HCF, remember, you can use the prime factor by this,

15:38 or you just pick all the values you have here, so when you pick all the values you have here,

15:43 you are expected to have the HCF which is going to be in this value, just take a look at it,

15:49 that will still give us, one, two, three, one, two, one, two, so you have seven, common, three,

15:59 common, two, common, so when you pick it up, if you look at it, it's still the same thing we have,

16:05 two times two, and then times three times seven, now, go up, now we move to the next part,

16:14 we move to the next part, the next part now is the square, square root, and perfect square,

16:20 when the division method would be able to get our 84, now the 84 using the two processes,

16:30 could have given you a very good idea, now let's pick up one more, one more, let's look into one more,

16:37 to be able to let's say find the is common factor of 24, 36, and 54, find the is common factors of 24,

16:47 36, and 54, now that's example two for the HCF, example two for the HCF, you have that's example four,

16:56 altogether HCF, so I'm picking the first one, 24, common factors that can take it two times two,

17:04 always split it into the power two, two times two, four times two, four times two, eight,

17:12 eight times three gives 24, but the next one, 36, can two start it up or three, okay, we start with

17:24 or two, two times two, that's four, four times three, four times three, that's 12, 12 times three,

17:34 that gives 36, so have 56, I have two times two, that's four, four times two, eight, and eight times

17:48 seven, 56, now if you look two, the number two appears twice in all the numbers, so two times two,

17:57 that's why the number three and number seven does not appear, now look at two, two appears, yeah,

18:06 the IS common factors among them, we have, look at it, two appears, two also appears, they are common,

18:19 but if you look at it, within the three, these three only appears, did not appear anymore,

18:24 two, it cannot be the IS common, so looking through the process, the IS, the HCF of this,

18:34 will give us two times two, which is what, four, but remember if it was the LCM or pick three,

18:44 we would pick seven, but in the SCF look at what is common or through the process,

18:49 in the three, three, if it is two, you look at what if it's two value, you look at what's common,

18:54 then you pick it up, now, we move on to the left part, what is called the square, square roots,

19:01 and perfect square, now, square, a square is the number that results from multiplying any number

19:08 by itself, that's a square, if you look at the box carefully, you can add that box carefully,

19:14 you would observe that how many boxes do we have, that means, size times size of the blue,

19:21 there's two sides, how many two sides and two sides, so two sides from the square, this is square,

19:28 why, because it has two sides and two sides, multiply by itself, that's a square,

19:32 so if I have two times two, that's four, so I can have two square is four, now, looking to, again,

19:42 on what's a square, now look at it, so I have from the area, I have sides multiply, multiply by sides,

19:54 what have a square, so if I have sides the same equal number of sides, I have two times two,

20:00 that's four, if I have three times three, three times three, that's nine, if I have four times four,

20:10 that gives me 16, now, what the perfect square, the perfect square is the number that results from

20:19 multiplying a whole number by itself, the number that results from multiplying a whole number by

20:27 itself, now, what a perfect square, looking to, look, look, look to the value, we have 10 perfect

20:33 square below, we have so we have a number that results from multiplying by itself, it perfect square,

20:38 so I have two times two, that's two years to pass, two is four, now, see what, I have a perfect square,

20:47 a result from itself, so if I have perfect square, for example,

20:51 it result from its square, from itself, so looking to, two rest of part two, resulting from itself,

20:59 that's two times two, that's four, three rest of part two, resulting from itself, that's nine,

21:05 remember that three times three, four rest of part two, resulting from itself, these are perfect square,

21:11 that's 16, five rest of part two, resulting from itself, that's 25,

21:17 they result from themselves, so it means that what I'm saying here is five times five,

21:22 so five times five is 25, so five rest of part two, they are perfect square because they result from

21:26 themselves, now, so I have six rest of part two, that's 36, resulting from itself, seven is about two,

21:33 that's 49, eight rest of part two, that's 64, nine rest of part two, that's 81, and 10 rest of part two,

21:42 that's 100, so if you now have 11 rest of part two that's 121, two, and 12 rest of part two, that'll be 144,

21:49 so it does go around it, as far as it's resulting from itself, it's called a perfect square,

21:55 now, look at the square root, how do we as attend this square root is the factor of a number

22:06 when multiplied by itself gives the number, a square root is the factor of a number,

22:13 that when you multiply it by itself, it still remains the number, now, look at up, look up we have

22:20 moved for the next, remember we started from square to perfect square then to square root,

22:28 the three are they are together, so moving up I have square root,

22:34 so if I have the square root of 49, it means that what I'm simply referring to here is

22:49 third of 49 is seven, because it results from itself, itself, itself, it means it results from itself,

22:56 now if I move ahead to 79, that's seven, how is it seven, because when I have 49 rest of part two

23:04 into the square root, so this can take off this, so I can have seven, so the factor results from itself

23:12 to give the product, express 1025 as a product of its prime factor, express 1025 as a product of its prime

23:29 factor, now how do you do this, carefully look at it carefully, you have one cell, use the division

23:36 method, by now it should be close to how you can use the division method in getting, division

23:41 method should be a method you should familiarize yourself with, because division method actually will

23:47 give you a eclip picture in case you don't know the prime factors, so now looking through the question,

23:54 I have pig division method, that's seven, pig division method, so I have what are we dividing,

24:03 I am dividing 1, 1, 0, 2, 5, into 3, now 3 into 1, 1, 0, 2, 5 will give me 3, 6, 7, 5,

24:17 2 can go, so pick 3, 3 again, 3, I'm not exhausted, I have into 36, I have 12, into 75, I have 25,

24:29 can 3 go again, 3 would have successfully going to 12, but it can't go into 25, so what can go

24:36 effectively now, I can take a 5, so I have 5, I will give me 245, if 5 again can go successfully,

24:48 I will give me 49, now once I have a 49, what can go now, 7, 7 into 49 will give me 7 and

24:58 finally I have 7, give me 1, if you look to the process with this division, look to the process,

25:05 it means that I have 3, 3, 5, 5, 7, 7, double double of each of them using the division method,

25:16 so we have the division method, so from the graph, from the table, we have 3, 3, that's 2, 3,

25:28 2, 5, 2, 7, now looking to means that I can write it up as 1, 1, 0, 2, 5 will give me 2, 3, 2,

25:43 multiply by 5, 2, multiply by 7, 2, let me split them into 2, let's split them into 2,

25:55 so split them into 2, I have 3 times 5 times 7, for the first part, and the second part, I have 3 times 5 times 7,

26:07 now splitting them into 2, 3 times 5, that's 15, 15 times 7, that is 1, 0, 5, multiply by 3 times 5, 15,

26:19 15 times 7, that is 1, 0, 5, now it means that these 2 are what we refer, so the final answer,

26:32 you just pick a 1, 1, 0, 5, is 1, 0, 5 is a product of the prime factors, remember 3, 5, 7 are the

26:43 prime factors of this value, 3, 5, 7, it's another prime factor of this value, now the product of the

26:53 prime factor, what you do in that, these 3, 3 will give this, this gives this, so you pick a 1,

27:01 so as the product of its prime factor, we're going to be having 1, 0, 5, that's 1, 0, 5,

27:09 so looking to, we have one more example that says find this smallest number by which 540

27:18 multiply, so that the product is a perfect square, find the number by which you multiply 540,

27:26 and the product is a perfect square, follow the same division, like I said, follow the same

27:32 division rule, you would all have the same pattern of question, follow the same division rule, now bring

27:40 out the book, that's the example, it's bring out the value, that's 540, okay, what can go, let's go

27:51 with 2, this factor 2 in 540, we have 270, we have 2, again we have 1, 3, 5, at 1, 3, 5, 3 can go

28:04 this point, 2 is exhausted, 3, we have 45, we have 3 again, we have 15, 3 is exhausted, now 5 can go

28:16 5, we have, we have 5, we have 3, up, up, sorry, take it up, we have, into 45, we have 15,

28:32 so I have my 3 again, that's 15, so by now, I can bring it up and say, okay, my 3 again, that's 3

28:43 times 5, as 15, then finally 5, 1, alright, you pick up this, what are your possible combination,

28:52 you will have 504, is 2 is to power, how many 2 do you have, you have 2, multiply by how many

29:02 3 do you have, 3, and multiply by 5, 5 we just 1, now looking through, what will be the possible

29:09 values that you can have, that will be looking at this, we will have 2, the indent of 3 and 5 are

29:17 odd, they are odd, number, so the number required is going to be what, 3, and what, 5, and 3 times 5

29:29 gives us what, 15, the value says the least, the least of, look at the question, says, multiply,

29:38 find the lowest number by which, 540, 540 can be multiplied by, so the question is, 540, how

29:47 do you multiply it by, so you 540 would go in 2 is to power, 2 is to power, 3 multiply by 5,

29:56 and a final answer gives us what, 15, now, our starting work with the evaluation, after the series

30:04 of lectures, or the series of teachings that have been done, so LCM and ECF, so question number 1 says,

30:11 determine the LCM of the following set of numbers, 24 and 60, question number 1, that's

30:19 1, 1, 2, 12, 18, and 40, the LCM, then question 2, determine the HCF of the following set of numbers,

30:30 40 and 64, determine the ACF of the set of numbers, 40 and 64, thank you very much for watching,

30:41 my name is Oya Sesson, until next time.