Question

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

2
2

0
0

1
1

3

Answer 1

To determine the exponent of the prime factor 3 in the prime factorization of 54, we first need to find the prime factors of 54.

54 can be factored as follows:

1. Divide by 2 (the smallest prime number):
\[
54 \div 2 = 27
\]

2. Next, we factor 27. Since it is an odd number, we will use the next smallest prime, which is 3:
\[
27 \div 3 = 9
\]

3. We factor 9 next:
\[
9 \div 3 = 3
\]

4. Finally, we factor 3:
\[
3 \div 3 = 1
\]

Now, we can write the prime factorization of 54:
\[
54 = 2^1 \times 3^3
\]

In this factorization, the exponent of the prime factor 3 is 3.

Thus, the exponent of the prime factor 3 when expressing the prime factorization of 54 is **3**.