Assignment: Using Prime Factorization Investigation

Express each of these sums in the form a (b + c) where b and c do not have a common factor. Show all work.

1. 6 + 21

2. 27 + 45

3. 32 + 48

4. 30 + 75

5. 88 + 24

3 (2 + 7) 9 (3 + 5) 16 (2 + 3) 15 (2 + 5) 8 (11 + 3)

Step-by-step explanation:

6 + 21 = 2·3 + 3·7 = 3 (2 + 7) 27 + 45 = 3^3 + 3^2·5 = 9 (3 + 5) 32 + 48 = 2^5 + 2^4·3 = 16 (2 + 3) 30 + 75 = 2·3·5 + 3·5^2 = 15 (2 + 5) 88 + 24 = 2^3·11 + 2^3·3 = 8 (11 + 3)

In each case, the factor outside parentheses is the greatest common factor, the product of the prime factors common to both numbers. When the same factor has different powers, the least power is the common factor.