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OUR LESSON : FACTORSOUR LESSON : FACTORS

Hello Scarlet

This is Mrs. Bisanz

I will be your teacher today

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Warm Up

1. 230.21 x 3.15 = 725.16

2. 6.23 / 2.01 = 3.099

3. 12.89 – 2.991 = 9.899

4. 43.23 + 4.67 = 47.9

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What are Factors

A whole number that divides exactly into another whole number is called a factor of that number.

For example 20 / 5 = 4So, 5 is a factor of 20 as it divides exactly into 20.

20 / 4 = 5

So, 4 is a factor of 20 as it divides exactly into 20.

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If a number can be expressed as a product of two whole numbers, then the whole numbers are called factors of that number.

20 = 1 x 20 = 2 x 10 = 4 x 5

So, the factors of 20 are 1, 2, 4, 5, 10 and 20.

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Lets take another Example

List all the factors of 42.

So, the factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.

42 = 1 x 42

2 x 21

3 x 14

6 x 7

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How do we check if a number is a factor of another number

Is 7 a factor of 15?

We divide 15 by 7 and check if remainder is zero 27 ) 15 14 1

As the remainder is 1 we conclude that 7 is not a factor of 15.

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A number is divisible by …

… 2 if the number is even.

… 3 if the sum of the digits within the number is divisible by 3. For example, the number 12,546 is divisible by 3 because 1+2+5+4+6 or 18 is divisible by 3.

… 4 if the number formed by the last two digits of the number is divisible by 4. For example,67,984 is divisible by 4 because 84 is divisible by 4.

… 5 if the number ends with either a 0 or 5.

… 6 if the number passes the divisibility tests for both 2 and 3. In other words, it must be even and the sum of its digits must be divisible by 3.

RULES

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A number is divisible by …

… 7 if the difference of the number formed by removing the last digit and two times that last digit is divisible by 7. For example, 3794 is divisible by 7 because 379 – 2(4) or 371 isdivisible by 7. If this is not clear repeat the process again using thenumber 371: 37 –2(1) or 35.

… 8 if the number formed by the last three digits of the number is divisible by 8. For example, 2,657,128 is divisible by 8 because 128 is divisible by 8.

… 9 if the sum of the digits within the number is divisible by 9. For example, the number 12,546 is divisible by 9 because 1+2+5+4+6 or 18 is divisible by 9.

RULES

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A number is divisible by …

… 10 if the number ends with 0.

… 11 if the difference of the sum of every other digit within the number and the sum of the remaining digits within the number is divisible by 11. For example, the number 40,865 is divisible by 11 because (4+8+5) – (0+6) or 17 – 6 or 11 is divisible by 11.

… 12 if the number passes the divisibility tests for both 3 and 4. In other words, the sum of the digits must be divisible by 3 and thenumber formed from the last two digits of the number must be divisible by 4.

RULES

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and finally a number is divisible by 13 If the sum of the number formed by removing the last digit andfour times that last digit is divisible by 13.

For example, 7384 is divisible by 13 because 738 + 4(4) or 754 isdivisible 13. If this is not clear repeat the process again using the number 754: 75 + 4(4) or 91. If this is not clear repeat the process again using the number 91: 9 + 4(1) or 13.

RULES

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By remembering these rules we can find out factors of any number

Lets take an example : Find Factors of 156

2: yes; It’s a even number

3: yes; as 1 + 5 + 6 = 12 is divisible by 3

4: yes; as last 2 digits 56 is divisible by 4

5: No; the ones digit is not 0 or 5

6: Yes as the number by 2 and 3

7: No it is not divisible

8: No it is not divisible

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9: No as the sum of digits is 12 and it is not divisible by 9

10: No; As the ones digit is not 0

12: Yes as the number is divisible by 3 and 4

We get the factors as 2, 3, 4, 6, 12, 13 as 12 x 13 = 156

Example conti…

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Now you try some !

Determine whether the first number is divisible by thesecond number

1) 2,641 ; 3 no

2) 60,003 ; 3 no

3) 6780 ; 10 yes

4) 42,981 ; 2 no

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Break Time

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Game time

Click here to play a game

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1. If $256 was divided amongst Ben and his three brothers,how much will each get ? Will some money be left after equal distribution ? What can you say about 4 and 256 ?

$256 divided by 4 gives $64 per person. All money will be equally distributed and no money will be left balance , this means that 4 is a factor of 256

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2. 39 baseball bats were received in the school for practice.In how many least number of teams can they be distributed equally?

It can be distributed in 3 teams as it is the lowest factor

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3. Find two numbers that are divisible by both of the given

2 and 9 , 6 and 10 , 5 and 9

a.18, 36

b.30, 60

c. 45, 90

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Let us review what we have learnt today

A whole number that divides exactly into another whole number is called a factor of that number.

If a number can be expressed as a product of two whole numbers, then the whole numbers are called factors of that number.

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To check if a number is a factor of another number we divide the larger number with the smaller number and if we get no remainder then we can conclude that the smaller number is a factor of the larger number

For example 20 / 5 = 4 so here remainder = 0

Hence 5 is a factor of 20

Review

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Great Job Today!

Remember to practice what you learned!