GOAL 2:DIVISORS,

MULTIPLES AND FACTORS

DIVISIBILITY RULES

DIVISORSDIVISORS

How many divisors does a number have?

Suppose you wish to find the number of divisors of 48. Starting with 1 we can work through the set of natural numbers and test divisibility in each case, noting that divisors

can be listed in factor pairs.

48 = 1×48 = 2×24 = 3×16 = 4×12 = 6×8

44

As we can see, 6 can be written as product of two numbers in many ways: 6 = 1 × 6

6 = 2 × 3

6 = 3 × 2

6 = 6 × 1

1, 2, 3 and 6 are exact divisors of 6

MULTIPLESThe products of a number with the natural numbers 1,2,3,4,5, …. Are called MULTIPLES of a number.

For example:7x1=7 7x2=14

7x5=35So the multiples of 7 are 7, 14 and 35 and so on.

The multiples of a number are obtained by multiplying the number by each of the natural numbers.

For example:multiples of 4 are 4, 8, 12, 16, …

6

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 = 15,30,4,60,75,90,105,120,135,……

The number of multiples of a given number is infinite.

7 divides 28 exactly and gives Quotient 4 and

Remainder 0.

28 ÷ 7 = 4

4 divides 28 exactly and gives Quotient 7 and

Remainder 0.

28 ÷ 4 = 7

28 divides 28 exactly and gives Quotient 1 and Remainder 0.

28 ÷ 28 = 1

FACTORS

28 ÷ 1 = 28

28 ÷ 4 = 7

28 ÷ 7 = 4

28 ÷ 28= 1

1

4

7

28

FACTORS OF 28

16 ÷ 1 = 16

16 ÷ 2 = 8

16 ÷ 4 = 4

16 ÷ 8 = 2

16 ÷ 16 = 1

1

2

4

8

16

FACTORS OF 16

FACTOR

A factor of a number is an exact

divisor of that number i.e. the factor

leaves remainder 0 when it divides

the number.

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.

FACTORS OF SOME NUMBERS

8 = 1,2,4,8

16 = 1,2,4,8,16

25 = 1,5,25

4 × 5 = 20

Factors Multiple

POINTS TO REMEMBER

• 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.

• Every multiple of a number is greater than or equal to that number.

• The number of multiples of a given number is infinite.

• Every number is a multiple of itself.

POINTS TO REMEMBER

THANK YOU