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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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.

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