Question
fewrite 92 and 146 as products of their prime factors
Ask by Adkins Garrett. in South Africa
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
92 can be written as \(2 \times 2 \times 23\) and 146 as \(2 \times 73\).
Solution
1. **Factorize 92**
- Divide 92 by 2:
\[
92 \div 2 = 46
\]
- Divide 46 by 2:
\[
46 \div 2 = 23
\]
- Since 23 is a prime number, the factorization stops here.
\[
92 = 2 \times 2 \times 23 = 2^2 \times 23
\]
2. **Factorize 146**
- Divide 146 by 2:
\[
146 \div 2 = 73
\]
- Since 73 is a prime number, the factorization stops here.
\[
146 = 2 \times 73
\]
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Simplify this solution Beyond the Answer
To break down 92 into its prime factors, we start by dividing it by the smallest prime number, which is 2. So, 92 ÷ 2 = 46. We can then divide 46 again by 2 to get 23. Since 23 is a prime number, we stop there. Therefore, the prime factorization of 92 is 2 × 2 × 23, or \(2^2 \times 23\). For 146, we again start with the smallest prime, which is 2. Dividing 146 by 2 gives us 73. Since 73 is also a prime number, we stop here, leading to a prime factorization of 146 as 2 × 73. In summary: 92 = \(2^2 \times 23\) 146 = \(2 \times 73\)
