Find the prime factorization of the number (use the divisibility tests where helpful). $72$
A) $2 \cdot 2 \cdot 3 \cdot 3 \cdot 7$
B) $2 ^ { 3 } \cdot 3 \cdot 3$
C) $2 \cdot 2 \cdot 2 \cdot 13$
D) $2 \cdot 2 \cdot 2 \cdot 3 \cdot 7$
E) $2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$

Question

Quizplus · Accepted Answer

We can use the divisibility test for 3 to see that 7+2=9 is divisible by 3, so 72 is divisible by 3. Therefore, we can factor out $3$ to get $72 = 3 \cdot 24$. Then, we can use the fact that $24$ is divisible by $2$ to get $24=2\cdot 12$, and $12$ is also divisible by $2$ to get $12 = 2 \cdot 6$. Finally, we see that $6$ is divisible by $2$ and $3$, so we can write $6 = 2 \cdot 3$. Putting it all together, we have $$72 = 3 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 = 2^3 \cdot 3^2,$$ so the answer is $\boxed{\textbf{(E)}}$.

Find the Prime Factorization of the Number (Use the Divisibility 727272

Find the Prime Factorization of the Number (Use the Divisibility $72$