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We can see that 12 can be found by multiplying 1 and 12; 2 and 6; and 3 and 4. Example 2: Find the factors of: (a) 24 (b) 36
That is, 12 = 1 × 12 = 12 × 1, 12 = 2 × 6 = 6 × 2, 12 = 3 × 4 = 4 × 3 Solution: (a) 1 × 24 = 24 (b) 1 × 36 = 36
Be Aware
Thus, the numbers 1, 2, 3, 4, 6 and 12 are the factors of 12. 2 × 12 = 24 2 × 18 = 36 Stop the process when

Hence, we can say that when we multiply two numbers to get a 3 × 4 = 12 3 × 8 = 24 3 × 12 = 36 the same factors are
product, the numbers being multiplied are called factors. 4 × 6 = 24 4 × 9 = 36 there in a multiplication
fact.
In other words, any number is a factor if it exactly divides the given Factor Product 6 × 6 = 36
number, leaving no remainder. Thus, the factors of 24 are Thus, the factors of 36 are
Example: 2 12 6 ; 3 12 4
12 12 1, 2, 3, 4, 6, 8, 12 and 24. 1, 2, 3, 4, 6, 9, 12, 18 and 36.
0 0 Using Division

So, 2, 6 and 3, 4 are the factors of 12.
To find the factors of a number using division, divide Think Tank
the number by each of the possible counting numbers.
Think Tank Critical Thinking Can a number have only one
Example 3: Find all the factors of 60. factor? Which number is it?
There are 24 cells in Solution: We divide 60 by all possible counting numbers.
each rectangle. Find
the multiplication 60 ÷ 1 = 60 ; 1 and 60 are factors of 60. 1 2 3 4 5 6 10 12 15 20 30 60
fact for each. Then,
list the factors 60 ÷ 2 = 30 ; 2 and 30 are factors of 60.
of 24 using these 60 ÷ 3 = 20 ; 3 and 20 are factors of 60.
multiplication facts.
60 ÷ 4 = 15 ; 4 and 15 are factors of 60.
Be Aware
60 ÷ 5 = 12 ; 5 and 12 are factors of 60. Continue the process of
Finding the Factors of a Number 60 ÷ 6 = 10 ; 6 and 10 are factors of 60. division till the quotient is

The factors of a number can be found by either multiplication or division. All possible divisions are being tried out. larger than the divisor.

Using Multiplication Thus, 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 are factors of 60.

To find the factors of a number using multiplication, we look for numbers whose Example 4: Write all the factors of 30.
product is the given number. Solution: 30 ÷ 1 = 30 1 × 30 = 30

Example 1: Find the factors of 48. 30 ÷ 2 = 15 or 2 × 15 = 30

Solution: 1 × 48 = 48; 1 and 48 are factors 30 ÷ 3 = 10 3 × 10 = 30
of 48. 1 2 3 4 6 8 12 16 24 48 30 ÷ 5 = 6 5 × 6 = 30
2 × 24 = 48; 2 and 24 are factors Thus, the factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.
of 48.

3 × 16 = 48; 3 and 16 are factors of 48. to Find out Whether one Number is a Factor of another

4 × 12 = 48; 4 and 12 are factors of 48. We know that for a number to be a factor of another number, it must exactly divide
6 × 8 = 48; 6 and 8 are factors of 48. the larger number without leaving any remainder.

There are no more pairs of numbers whose product is 48. Example 5: Check whether the first number is a factor of the second number.
So, 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 are all factors of 48. (a) 7, 80 (b) 12, 144

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