what is the sum 36 + 45 as the product of their GCF and another sum.

Answer 1

The factors of 36 are 2,2,3,3 and 45 is 3,3,5

The greatest common factor is the product of all of the factors common to both.

3 is common, and found twice in each, so we use the product, 3 x 3 or 9

Using the distribution rule ab + ac = a(b + c)

We can say 36 + 45 is also 2x2x3x3 + 3x3x5

Removing the common factors, 3 and 3 or the GCF 9 we have:

3x3(2x2) + 3x3(5) or 9(2x2) + 9(5) (Read this as 3 times 3 times 2 times 2 plus 3 times 3 times 5)

9(4) + 9(5) (nine times four plus nine times five)

By the distribution property, 9(4+5) [Is the same as nine times (four plus five)]