Factors and Multiples

Factors

( Year 5 Revision)

What is a Factor?

The factors of a particular number are those individual numbers we multiplied before we could get that particular number.

In this example, the factors of 4 are 1, 2 and 4.

Multiple Choice

Select a number which is not a factor of 10?

• 4

• 2

• 1

• 5

Multiple Choice

Which of these is not a factor of 12?

• 3

• 2

• 6

• 5

Multiple Choice

1 , 2 , 3 , 6 , 9 are all factors of

• 16

• 18

• 12

• 24

Factors

A factor also divides a number completely without leaving any remainder.

Factors of 4 = 1, 2 and 4
Try dividing 4 by 1 , 2 and 4 and check to see there are no remainders. 

Prime and Composite

Prime numbers are whole numbers having only two different factors: 1 and itself.

Composite numbers have more than two different factors.

Multiple Select

Select all the prime numbers from the list below..

• 11

• 12

• 13

• 14

• 15

Multiple Select

Select the prime numbers among the following:

• 14

• 5

• 6

• 7

• 8

Multiple Select

____ is the smallest prime number.

• 1

• 2

• 3

• 4

• 5

Multiple Select

Select the composite numbers from the list below:

• 21

• 23

• 25

• 27

• 29

Multiple Select

Select the prime numbers from the list below:

• 31

• 33

• 35

• 37

• 39

Multiple Select

18 is an example of _________ numbers.

• prime

• composite

Multiple Select

Select the composite numbers from the list below:

• 21

• 23

• 25

• 27

• 29

Multiple Select

Select the prime numbers from the list below:

• 19

• 12

• 13

• 14

• 15

Multiple Select

Which of the following numbers are prime numbers?

• 11

• 12

• 13

• 15

Still on Factors

• The factors of a number include all divisors of that number. The factors of 8, for example, are 1, 2, 4 and 8. You can divide 8 by any of these numbers and obtain another whole integer number (i.e no remainder)

• Prime numbers have only two different factors. For example, 3, 5 and 7 are prime numbers

• Composite numbers are whole numbers which are not prime. This means that they have more than two different factors. For example, 4, 6, 8 and 10 are examples of composite numbers.

Common Factors

To determine the common factors of two or more numbers, we first list their individual factors out.

Then, we compare these factors and select those that are common.

C.F of 8 and 12 = 1, 2 and 4.
Highest Common Factor = 4

Multiple Select

Select the common factors of 12 and 16.

• 3

• 2

• 1

• 4

• 5

Multiple Select

Select the common factors of 18 and 24.

• 3

• 2

• 1

• 6

Multiple Select

Select the common factors of 8 and 24.

• 3

• 2

• 1

• 4

• 6

Multiple Select

What is the Highest Common Factor of 14 and 20?

• 5

• 2

• 1

• 7

More on Factors

• The number 1 is the smallest factor of every number.

• Every number will have a minimum of two factors, 1 and the number itself.

• A number that has only two factors, 1 and itself, is called a prime number.

Prime Factorization

• When we write a number as a product of all its prime factors, it is called prime factorization. For example, 12 = 2 x 2 x 3

• Every number used in prime factorization must be a prime number. e.g 2 x 2 x 3 Here, the 2s and 3 are all prime

• Sometimes to write the prime factors of a number we might have to repeat some of the factors (as shown above).

Example:

Express 24 as a product of its prime factors.

(Hint: Product means multiplication)

Answer: 24 = 2 x 2 x 2 x 3

Example:

Express 24 as a product of its prime factors in index form.

Answer: 24 = 2³ x 3¹

Example:

Find the H.C.F of 16 and 12.

Solution

In this method, we keep dividing 16 and 12 using PRIME NUMBERS which can go in both numbers without any remainder.

Example:

Find the largest number which when divided into 12 and 20 will leave no remainder .

Workings:

LARGEST number required here is the Highest Common Factor (H.C.F)

H.C.F of 12 and 20 = 2 x 2

= 4

Example:

Find the largest number which when divided into 20 and 26 will leave a remainder of 2 in each case.
(Hint: First we take away 2 from 20 and 26. Next, we find the H.C.F of the resulting numbers)
Answer = 6
CHECK: 20 $\div$ 6 = 3 remainder 2

             26 $\div$ 6 = 4 remainder 2
Notice a remainder of 2 in both instances.

Multiple Choice

Find the H.C.F of 18 and 20.

• 2

• 4

• 6

• 8

Multiple Choice

Find the H.C.F of 16 and 24.

• 2

• 1

• 6

• 8

Multiple Choice

Find the largest number which when divided into 15 and 20 will leave no remainder.

• 10

• 4

• 3

• 5

Multiple Choice

Find the largest number which when divided into 21 and 33 will leave a remainder of 3 in each instance.

• 6

• 11

• 3

• 7