Question

Write 54 as a product of prime factors
2×5×9
2×27
2×3×3×3
2×3×3×5

Answer 1

To express 54 as a product of prime factors, we can start by repeatedly dividing by the smallest prime numbers.

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

2. Next, factor 27. Since 27 is not divisible by 2, we move to the next prime number, which is 3:
\( 27 \div 3 = 9 \)

3. Now factor 9:
\( 9 \div 3 = 3 \)

4. Finally, factor the last 3:
\( 3 \div 3 = 1 \)

Now, putting it all together, we have:
\[ 54 = 2 \times 3 \times 3 \times 3 \]
or, in exponential form:
\[ 54 = 2 \times 3^3 \]

Thus, the prime factorization of 54 is:
\[ 54 = 2 \times 3 \times 3 \times 3 \]
So, from your options, the correct factorization is:
**2 × 3 × 3 × 3**.