Question
Express the prime factorization of 84 with exponents.(1 point)
Responses
3 ⋅4⋅7
3 times 4 times 7
2 ⋅ 3 ⋅ 7
2 times 3 times 7
22 ⋅ 3 ⋅ 7
2 squared times 3 times 7
2 ⋅ 32 ⋅7
Responses
3 ⋅4⋅7
3 times 4 times 7
2 ⋅ 3 ⋅ 7
2 times 3 times 7
22 ⋅ 3 ⋅ 7
2 squared times 3 times 7
2 ⋅ 32 ⋅7
Answers
GPT-4o mini
The prime factorization of 84 can be found by dividing it by the smallest prime numbers.
1. Start by dividing by 2:
\( 84 ÷ 2 = 42 \)
\( 84 = 2 × 42 \)
2. Divide 42 by 2 again:
\( 42 ÷ 2 = 21 \)
\( 84 = 2^2 × 21 \)
3. Now divide 21 by the next smallest prime number, which is 3:
\( 21 ÷ 3 = 7 \)
\( 84 = 2^2 × 3 × 7 \)
Thus, the complete prime factorization of 84 is:
\[ 2^2 × 3^1 × 7^1 \]
In exponent form, it is represented as \( 2^2 × 3 × 7 \).
Among the given responses, the correct answer expressed with exponents is:
**22 ⋅ 3 ⋅ 7** (This represents \( 2^2 \cdot 3^1 \cdot 7^1 \))
1. Start by dividing by 2:
\( 84 ÷ 2 = 42 \)
\( 84 = 2 × 42 \)
2. Divide 42 by 2 again:
\( 42 ÷ 2 = 21 \)
\( 84 = 2^2 × 21 \)
3. Now divide 21 by the next smallest prime number, which is 3:
\( 21 ÷ 3 = 7 \)
\( 84 = 2^2 × 3 × 7 \)
Thus, the complete prime factorization of 84 is:
\[ 2^2 × 3^1 × 7^1 \]
In exponent form, it is represented as \( 2^2 × 3 × 7 \).
Among the given responses, the correct answer expressed with exponents is:
**22 ⋅ 3 ⋅ 7** (This represents \( 2^2 \cdot 3^1 \cdot 7^1 \))