To find the greatest common factor, lets factor each monomial:
42m⁶
First, lets factor 42
42 | 2
21 | 3
7 | 7
1
42 = 2*3*7
Now, lets factor m⁶
m⁶ = m*m*m*m*m*m
So, 42m⁶=2*3*7*m*m*m*m*m*m
44m⁵
First, lets factor 44
44 | 2
22 | 2
11 | 11
1
44 = 2*2*11
Now, lets factor m⁵
m⁵ = m*m*m*m*m
So, 44m⁵ = 2*2*11*m*m*m*m*m
Now, lets compare both factors. The greatest common factor is the greatest factor both numbers have in common:
42m⁶ = 2*3*7*m*m*m*m*m*m
44m⁵ = 2*2*11*m*m*m*m*m
The greatest common factor is 2m⁵.