Factoring a Sum or Difference of Whole Numbers

We can have sums or differences of whole numbers; for example (26 + 65) or (48 − 16).

For factoring such sums or differences of whole numbers:

• We write the whole numbers as products of their prime factors.
• Then we factor out the greaterst common factors (gcf) from those numbers
• We factor out any given common factor, if required, from such sums or differences of whole numbers.

Example:

Factor out the gcf from the sum (28 + 63)

Solution

The prime factorization of 28 is 28 = 4 × 7

The prime factorization of 63 is 63 = 9 × 7

So the greatest common factor or gcf of 28 and 63 is 7

So (28 + 63) = (4 × 7 + 9 × 7) = 7(4 + 9)

Factor out the gcf from the sum of whole numbers (26 + 91)

Solution

Step 1:

26 = 2 × 13

91 = 7 × 13

Step 2:

The gcf of 26 and 91 is 13. So factoring out the greatest common factor 13

(26 + 91) = (2 × 13 + 7 × 13)= 13(2 + 7)

Factor out 6 from the difference of whole numbers (108 − 84)

Solution

Step 1:

84 = 2 × 2 × 3 × 7 = 6 × 14

108 = 2 × 2 × 3 × 3 × 3 = 6 × 18

Step 2:

So factoring out 6 from the difference of the given numbers

(108 − 84) = (6 × 18 − 6 × 14) = 6(18 − 14)