Question

What is the greatest common factor of 42a5b3, 35a3b4, and 42ab4?

Answer 1

To get the GCF of the the expression, we look for the greatest factor of the expression:
42a5b3, 35a3b4, and 42ab4?
thus
(42a5b3, 35a3b4, 42ab4)
factoring b^3 which is the GCF of (b^3,b^4,b^4)we get:
b^3(42a^5,35a^3b,42ab)
next we factor our a which is the GCF of (a^5,a^3,a)
ab^3(42a^4,35a^2b, 42b^4)
next we factor out 7 which is the GCF of (42,35,42)
7ab^3(6a^4,5a^2b,6b^4)
hence the GCF is:
7ab^3

Answer 2

`7ab^3`.

Explanation:

We have been given three expressions. We are asked to find the greatest common factor of our expressions.

`42a^4b^3`,
`35a^3b^4`,
`42ab^4`

The greatest common factor is the factor that divides two or more numbers.

Factors of coefficient:

42: 1, 2, 3, 6,7, 14, 21, 42

35: 1, 5, 7, 35

The greatest common factor of coefficient is 7.

Factors of
`a^5: a*a*a*a*a`

Factors of
`a^3: a*a*a`

Factors of
`a: 1*a`

The greatest common factor of
`a^5,a^3,a` is a.

Factors of
`b^3: b*b*b`

Factors of
`b^4: b*b*b*b`

The greatest common factor of
`b^3,b^4,b^4` is
`b^3`.

Upon combining all these factors, we will get
`7ab^3`.

Therefore, the greatest common factor of
`42a^4b^3`,
`35a^3b^4` and
`42ab^4` is
`7ab^3`.