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

Given:

42a^5b^3, 35a^3b^4, and 42ab^4

Determine the Greatest Common Factor (GCF)

Solution:

In order to determine the greatest common factor, we simply look at the factors of each coefficient,

42, 35 and 42 are all divisible by 7.

Now we need to determine the common variables since we have a and b. All values have a and b, and in order to know which is the greatest common factor, we will take the variable with the least degree, therefore for a, we will take a without any degree as exhibited in 42 ab^4, and for be, we will take b^3 since it has the least degree for b, exhibited in 42a^5b^3.

Now we can combine the values that we've factored.

= 7(a)(b^3)

= 7ab^3

The greatest common factor of the given values is 7ab^3

Given the equation:

42a^5b^3, 35a^3b^4 and 42ab^4

Determine the greatest common factor.

Solution:

In order to determine factor, we first need to list the factors of 42 and 35, and determine the GCF.

Factors of 42:

1, 2, 3, 6, 7, 14, 21, and 42.

Factors of 35:

1, 5, 7 and 35

It can be seen that the greatest common factor is 7. Now for the terms, we simply take the common term with the least degree or exponent.  In our case, we'll take a and b^3

= 7ab^3

Final answer:
= 7ab^3