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

Question

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.