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We can see that 12 can be found by multiplying 1 and 12; 2 and 6; and 3 and 4.
That is, 12 = 1 × 12 = 12 × 1, 12 = 2 × 6 = 6 × 2, 12 = 3 × 4 = 4 × 3

Thus, the numbers 1, 2, 3, 4, 6 and 12 are the factors of 12.

Hence, we can say that when we multiply two numbers to get a 3 × 4 = 12
product, the numbers being multiplied are called factors.

In other words, any number is a factor if it exactly divides the given Factor Product
number, leaving no remainder.
Example: 2 12 6 ; 3 12 4
12 12
0 0

So, 2, 6 and 3, 4 are the factors of 12.

Think Tank Critical Thinking

There are 24 cells in
each rectangle. Find
the multiplication
fact for each. Then,
list the factors
of 24 using these
multiplication facts.

Finding the Factors of a Number

The factors of a number can be found by either multiplication or division.

Using Multiplication

To find the factors of a number using multiplication, we look for numbers whose
product is the given number.

Example 1: Find the factors of 48.

Solution: 1 × 48 = 48; 1 and 48 are factors
of 48. 1 2 3 4 6 8 12 16 24 48
2 × 24 = 48; 2 and 24 are factors
of 48.

3 × 16 = 48; 3 and 16 are factors of 48.

4 × 12 = 48; 4 and 12 are factors of 48.
6 × 8 = 48; 6 and 8 are factors of 48.

There are no more pairs of numbers whose product is 48.
So, 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 are all factors of 48.

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