Factoring a Sum or Difference

Introduction

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 = 74+9Problem 1:

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 = 213+713= 132+7Problem 2:

Factor out 6 from the difference of whole numbers 10884

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

10884 = 618614 = 61814