Question

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find the greatest common factor of these three expressions.
$42y^2$, $12y^3$, and $18y^4$

Explanation:

Step1: Factor coefficients to primes

$42=2\times3\times7$, $12=2^2\times3$, $18=2\times3^2$

Step2: Find GCF of coefficients

Identify shared prime factors: $2^1\times3^1=6$

Step3: Find GCF of variable terms

For $y^2, y^3, y^4$, the lowest power is $y^2$

Step4: Combine GCFs

Multiply coefficient GCF and variable GCF

Answer:

$6y^2$