Find the prime factorization of the number below (use the divisibility tests where helpful). $78$
A) $2 \cdot 3 \cdot 19$
B) $2 \cdot 7 \cdot 13$
C) $2 \cdot 3 \cdot 13$
D) $2 \cdot 3 \cdot 23$
E) $2 \cdot 3 \cdot 13 \cdot 23$

Question

Quizplus · Accepted Answer

The divisibility test for 3 states that if the sum of the digits of a number is divisible by 3, then the number itself is divisible by 3. In this case, $7+8=15$, which is divisible by 3, so we know that 78 is divisible by 3. Dividing 78 by 3 gives us 26, and since 26 is not divisible by 2, we know that 78 cannot be divided by 4. Dividing 26 by 2 gives us 13, which is prime. Therefore, the prime factorization of 78 is $2 \cdot 3 \cdot 13$ or $\boxed{	extbf{(C)}}$.

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