Question

what is the gcf of $16s^{3}t$, $40s^{5}$, and $68t^{2}$?
○ 4
○ $4s^{3}t$
○ 8
○ $8s^{3}t$

Explanation:

Step1: Factor coefficients to primes

$16 = 2^4$, $40 = 2^3 \times 5$, $68 = 2^2 \times 17$

Step2: Find GCF of coefficients

The lowest power of 2 across all is $2^2 = 4$

Step3: Analyze variable $s$

Terms have $s^3$, $s^5$, and no $s$ (implies $s^0$). The lowest power is $s^0 = 1$

Step4: Analyze variable $t$

Terms have $t^1$, no $t$ (implies $t^0$), and $t^2$. The lowest power is $t^0 = 1$

Step5: Multiply GCF components

$4 \times 1 \times 1 = 4$

Answer:

4