Question

What is the GCF of 64a^8b^4 and 56a^5b^8

Answer 1

We need to find the greatest common factor of

`64a^8b^4,56a^5b^8`

We will find the greatest common factor of 64 and 56, first

Since the factors of 64 are

`\begin{gathered} 1*64 \\ 2*32 \\ 4*16 \\ 8*8 \\ 1,2,4,8,16,32,64 \end{gathered}`

Since the factors of 56 are

`\begin{gathered} 1*56 \\ 2*28 \\ 4*14 \\ 8*7 \\ 1,2,4,7,8,14,28,56 \end{gathered}`

Then the common factors are 1, 2, 4, 8

The greatest is 8, then

The GCF of 64 and 56 is 8

The greatest common factor of the same variables is the least power

Then the GCF of a^8 and a^5 is a^5

The GCF of b^4 and b^8 is b^4

Then the greatest common factor of the given terms is

`\text{GCF}=8a^5b^4`