Question
1 Rewrite 92 and 146 as products of their prime factors.
Ask by Colon Evans. in South Africa
Mar 12,2025
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. **Factorizing 92:**
- First, divide by \(2\) since \(92\) is even:
\[
\frac{92}{2} = 46
\]
- \(46\) is also even, so divide by \(2\) again:
\[
\frac{46}{2} = 23
\]
- \(23\) is a prime number.
Therefore, the prime factorization of \(92\) is:
\[
92 = 2 \times 2 \times 23 = 2^2 \times 23
\]
2. **Factorizing 146:**
- \(146\) is even, so divide by \(2\):
\[
\frac{146}{2} = 73
\]
- \(73\) is a prime number.
Therefore, the prime factorization of \(146\) is:
\[
146 = 2 \times 73
\]
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Simplify this solution Beyond the Answer
To express 92 as a product of its prime factors, we start by dividing it by the smallest prime number, which is 2: 92 ÷ 2 = 46 46 ÷ 2 = 23 Since 23 is a prime number, we can express 92 as: 92 = 2² × 23. Now for 146, we again start by dividing by 2: 146 ÷ 2 = 73. Since 73 is also a prime number, we can express 146 as: 146 = 2 × 73. So, the prime factorization of 92 is 2² × 23, and for 146, it is 2 × 73.
