Question

Sofia wants to use the distributive property to rewrite the addition problem shown so that the numbers inside the parentheses have no common factor except 1.

(54+81)

Which is an equivalent expression that has numbers in the parentheses whose only common factor is 1?

A. 3(18 + 27)
B. 9(6 + 9)
C. 27(2 + 3)
D. 81(1 + 1)

Answer 1

C. 27(2 + 3)

Because gcd(54, 81) = 27, factor out 27: 54 + 81 = 27(2 + 3). The numbers 2 and 3 have no common factor besides 1.