Question

Write the sum of 18+27 as the product of their gcf and another sum

Answer 1

One possible answer is:

9×(2+3)

Explanation:

First we find the sum of 18 and 27. 18+27 = 45.

Next we find the GCF of 18 and 27. We do this by finding the prime factorization of each:

18 = 2*9

9 = 3*3

Thus, 18 = 2*3*3.

27 = 3*9

9 = 3*3

Thus, 27 = 3*3*3

We want the common factors; there are 2 3's in common, so 3*3 = 9 is the GCF. This makes the product 9×( ). The missing number would be 5, since 9*5 = 45. Writing this as a sum, we can use 2+3; this gives us 9×(2+3).

Answer 2

Factors of 18: 1; 2; 3; 6; 9; 18

Factors of 27: 1; 3; 9; 27

GCF(18; 27) = 9

18 + 27 = 9 × 2 + 9 × 3 = 9 × (2 + 3)