What is the prime factorization of 84?

Question

2 times 3 times 7
2 squared times 3 times 7
2 Superscript 5 Baseline times 3
2 squared times 21

Answer 1

The prime factorization of 84 can be found by dividing it by the smallest prime numbers.

1. Start with 84 and divide by 2 (the smallest prime): \( 84 \div 2 = 42 \)

2. Divide 42 by 2 again: \( 42 \div 2 = 21 \)

3. Now, divide 21 by the next smallest prime number, which is 3: \( 21 \div 3 = 7 \)

4. Finally, 7 is a prime number.

Putting this together, the prime factors of 84 are: \( 2 \times 2 \times 3 \times 7 \)

This can also be written in exponential form as: \( 2^2 \times 3^1 \times 7^1 \)

Thus, the prime factorization of 84 is: 2 squared times 3 times 7.

So, the correct choice from your options is: 2 squared times 3 times 7.