Question

Determine the exponent of the prime factor 3 when expressing the prime factorization of 54.(1 point)
Responses

2
2

1
1

3
3

0

Answer 1

To determine the exponent of the prime factor 3 in the prime factorization of 54, we first need to factor 54 into its prime components.

Starting with 54:

1. We can divide 54 by 2 (the smallest prime number):
\[
54 \div 2 = 27
\]
So, 54 can be expressed as \( 54 = 2 \times 27 \).

2. Next, we factor 27:
\[
27 \div 3 = 9 \quad \text{(because 27 is divisible by 3)}
\]
\[
27 = 3 \times 9
\]

3. Now we factor 9:
\[
9 \div 3 = 3
\]
\[
9 = 3 \times 3
\]

Putting it all together, we have:
\[
54 = 2 \times 3 \times 3 \times 3 = 2 \times 3^3
\]

From the factorization, we see that the prime factor 3 appears 3 times. Thus, the exponent of the prime factor 3 in the prime factorization of 54 is:

\[
\boxed{3}
\]