The greatest common factor is the biggest number that divides all of them evenly. For this, we have [tex]x^4, x^7, x^8[/tex]. Let's try [tex]x^4[/tex]. Does it divide all three evenly?
[tex]x^4/x^4 = 1\\x^7/x^4 = x^3\\x^8/x^4 = x^4[/tex]
Yes, because those are all whole numbers. Is there a bigger number than [tex]x^4[/tex] which divides all three? No, there can't be, because then it wouldn't go into [tex]x^4[/tex] evenly. (It would be too big.)
So [tex]$\boxed{x^4}$[/tex] must be the greatest common factor.
