1

Product – An answer to a multiplication problem.

7 x 8 = 56

Product2

Factor – a number that is multiplied by another to give a product.

7 x 8 = 56

Factors3

Factor – a number that divides evenly into another.

56 ÷ 8 = 7

Factor4

6 x 7 = 427 x 9 = 638 x 6 = 48

4 x 9 = 36

6 & 77 & 98 & 64 & 9

5

42 ÷ 7 = 663 ÷ 9 = 748 ÷ 6 = 8

36 ÷ 9 = 4

7969

6

7

FACTORS OF SOME NUMBERS

8 = 1x8, 2x4

Factors of 8: 1, 2, 4, 8

16 = 1x16, 2x8, 4x4

Factors of 16 : 1, 2, 4, 8, 16

25 = 1 x25, 5x5,

Factors of 26: 1, 5, 25

8

4 × 5 = 20

4 and 5 are factors of 20. We can also say that 20 is multiple of 4 and 5.

In 2 × 12 = 24,

2 and 12 are factors of 24.

24 is the multiple of 2 and 12.

So, a number is a multiple of its factors.

9

4 × 5 = 20

Factors Multiple

10

Multiples of 2 = 2,4,6,8,10,12,14,16,18,20,22,24…

Multiples of 3 = 3,6,9,12,15,18,21,24,27,30,33,36,…

Multiples of 15 = 15,30,45,60,75,90,105,120,135,……The number of multiples of a given number is infinite.

1 is a factor of every number.

Every factor of a number is an exact divisor of that number.

Every factor is less than or equal to the given number.

Number of factors of a given number are finite.

11

1212

FACTOR OR MULTIPLE?FACTOR OR MULTIPLE? For each of numbers in the statements, select For each of numbers in the statements, select

either multiple [M] or factor [F]either multiple [M] or factor [F] 34 34 × 5 = 170× 5 = 170 [[F] [] [M] [] [F] [] [M] [] [F] [] [M]]

25 × 4 = 10025 × 4 = 100 [[F] [] [M] [] [F] [] [M] [] [F] [] [M]]

90 × 10 = 90090 × 10 = 900 [[F] [] [M] [] [F] [] [M] [] [F] [] [M]]

45 × 6 = 27045 × 6 = 270 [[F] [] [M] [] [F] [] [M] [] [F] [] [M]]

7 × 30 = 2107 × 30 = 210 [[F] [] [M] [] [F] [] [M] [] [F] [] [M]]

1313

State whether the following State whether the following statements are statements are TRUETRUE or or FALSEFALSE

1. 1 is a factor of every number. 1. 1 is a factor of every number. F T

2. The largest factor of any number is the number itself. 2. The largest factor of any number is the number itself. F T

3. Number of factors of a given number is infinite. 3. Number of factors of a given number is infinite. F T

4.The number of multiples of 5 is 10. 4.The number of multiples of 5 is 10. F T

5.The factors of 65 are 1, 5 and 13 only. 5.The factors of 65 are 1, 5 and 13 only. F T

1414

CORRECTCORRECT

1515

WRONGWRONG

Prime Number – a number that has only two factors, 1 and itself.

77 is prime because the only

numbersthat will divide into it evenly are

1 and 7. 16

2, 3, 5, 7, 11, 13, 17, 19

Special Note:

One is not a prime number.

17

Composite number – a number that has more than two factors.

8

The factors of 8 are 1, 2, 4, 8

18

4, 6, 8, 9, 10, 12, 14, 15

Special Note:Every whole number from 2 on

is either composite or prime.19

Special Note:

One is not a prime nor a composite number.

It is not primebecause it doesnot have exactly

two differentfactors.

It is not composite

because it doesnot have morethan 2 factors.

20

21

The greatest common factor is the largest common factor of two numbers.

Factors are all of the numbers that divide into a given number equally.

The greatest common factor can be found by comparing all the factors of two numbers or by finding the prime

factorization of two numbers

22

Finding the factors of a number can be done by sequentially dividing numbers into the product. When the factors begin to repeat

you have found all factors.

23

Find the factors of 18 1 goes into 18, 18 times. 2 goes into 18, 9 times. 3 goes into 18, 6times.

4 does not divide 18 evenly. 5 does not divide 18 evenly.

We are now back to 6. We have found all factors of 18.

1, 2, 3, 6 and 18

24

Determine the greatest common factor of two numbers by finding all the factors for the two numbers then comparing them. The largest common factor of the two

numbers is their greatest common factor.

25

Find the GCF of 36 and 24

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18 and 36Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24

The greatest common factor is of 36 and 24 is 12

26

Find the factors of 48, 24 & 36

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

The common factors are

1, 2, 3, 4, 6, and 12.

ANSWER

EXAMPLE

The greatest common factor of 48, 24, and 36 is 12.

1, 2, 3, 4, 6,

1, 2, 3, 4, 6,

1, 2, 3, 4, 6, 12

12

12The GCF is 12.

27

Find the GCF of 15 and 100

Factors of 15: 1, 3, 5 and 15Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100

The greatest common factor of 15 and 100 is 5

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