1. GOAL 2:
DIVISORS,
MULTIPLES AND
FACTORS

2. DIVISIBILITY RULES

3. 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

4. 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

5. MULTIPLES
The 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=35
So 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. 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. 7 divides 28 exactly and
gives Quotient 4 and
Remainder 0.
28 ÷ 7 = 4

8. 4 divides 28 exactly and
gives Quotient 7 and
Remainder 0.
28 ÷ 4 = 7

9. 28 divides 28 exactly and
gives Quotient 1 and
Remainder 0.
28 ÷ 28 = 1

10. FACTORS

11. 28 ÷ 1 = 28
28 ÷ 4 = 7
28 ÷ 7 = 4
28 ÷ 28= 1
1
4
7
28
FACTORS OF 28

12. 16 ÷ 1 = 16
16 ÷ 2 = 8
16 ÷ 4 = 4
16 ÷ 8 = 2
16 ÷ 16 = 1
1
2
4
8
1
FACTORS OF 16

13. 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.

14. 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.

15. FACTORS OF SOME
NUMBERS
8 = 1,2,4,8
16 = 1,2,4,8,16
25 = 1,5,25

16. 4 × 5 = 20
Factors Multiple

17. 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.

18. • 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

19. THANK YOU