Question

Assignment: Using Prime Factorization Investigation

Answer 1

Answer:

1. 3(2 +7)
2. 9(3 +5)
3. 16(2 +3)
4. 15(2 +5)
5. 8(11 +3)

Step-by-step explanation:

1. 6 + 21 = 2·3 + 3·7 = 3(2 +7)
2. 27 + 45 = 3^3 + 3^2·5 = 9(3 +5)
3. 32 + 48 = 2^5 + 2^4·3 = 16(2 +3)
4. 30 + 75 = 2·3·5 + 3·5^2 = 15(2 +5)
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.