Answer:
[tex]\large\boxed{7ab}[/tex]
Step-by-step explanation:
[tex]14a^3b^4-7ab^7+21a^2b\\\\14a^3b^4=2\cdot\boxed7\cdot\boxed{a}\cdot\boxed{b}\cdot b\cdot b\cdot b\\\\7ab^7=\boxed7\cdot\boxed{a}\cdot\boxed{b}\cdot b\cdot b\cdot b\cdot b\cdot b\cdot b\\\\21a^2b=3\cdot\boxed7\cdot\boxed{a}\cdot a\cdot\boxed{b}\\\\GCF(14a^3b^4,\ -7ab^7,\ 21a^2b)=\boxed7\cdot\boxed{a}\cdot\boxed{b}=7ab[/tex]
