Question

what is the greatest common factor of $42a^5b^3$, $35a^3b^4$, and $42ab^4$?
$\bigcirc\\ 7ab^3$
$\bigcirc\\ 6a^4b$
$\bigcirc\\ 42a^5b^4$
$\bigcirc\\ 77a^8b^7$

Explanation:

Step1: Find GCF of coefficients

Factor 42, 35, 42:
42 = 2×3×7, 35 = 5×7, 42 = 2×3×7.
GCF of 42, 35, 42 is 7.

Step2: Find GCF of \(a\)-terms

For \(a^5\), \(a^3\), \(a\):
The smallest exponent of \(a\) is 1 (from \(ab^4\)). So GCF for \(a\) is \(a^1 = a\).

Step3: Find GCF of \(b\)-terms

For \(b^3\), \(b^4\), \(b^4\):
The smallest exponent of \(b\) is 3 (from \(42a^5b^3\)). So GCF for \(b\) is \(b^3\).

Step4: Combine GCFs

Multiply the GCFs: \(7 \times a \times b^3 = 7ab^3\).

Answer:

A. \(7ab^3\)