Q:

Write the sum of the numbers as the product of their GCF and another sum.44 + 40 =13 + 52 =15 + 81 =64 + 28 =​

Accepted Solution

A:
Answer:See explanationStep-by-step explanation:1. Find the GCF of 40 and 44:[tex]40=\underline{2\cdot 2}\cdot 2\cdot 5\\ \\44=\underline{2\cdot 2}\cdot 2\cdot 11\\ \\GCF(40,44)=2\cdot 2=4[/tex]So,[tex]40+44=4\cdot 10+4\cdot 11=4\cdot (10+11)[/tex]2. Find the GCF of 13 and 52:[tex]13=\underline{13}\\ \\52=2\cdot 2\cdot \underline{13}\\ \\GCF(13,52)=13[/tex]So,[tex]13+52=13\cdot 1+13\cdot 4=13\cdot (1+4)[/tex]3. Find the GCF of 15 and 81:[tex]15=\underline{3}\cdot 5\\ \\81=\underline{3}\cdot 3\cdot 3\cdot 3\\ \\GCF(15,81)=3[/tex]So,[tex]15+81=3\cdot 5+3\cdot 27=3\cdot (5+27)[/tex]4. Find the GCF of 64 and 28:[tex]64=\underline{2\cdot 2}\cdot 2\cdot 2\cdot 2\cdot 2\\ \\28=\underline{2\cdot 2}\cdot 7\\ \\GCF(64,28)=2\cdot 2=4[/tex]So,[tex]64+28=4\cdot 16+4\cdot 7=4\cdot (16+7)[/tex]