Question

what is the prime factorization of 246?
2·3·123
2·3·41·123
6·41
2·3·41

Explanation:

Step1: Check if factors are prime

Prime factorization requires all factors to be prime numbers (numbers greater than 1 with no divisors other than 1 and themselves).

• For \(2 \cdot 3 \cdot 123\): 123 is not prime (123 = 3×41), so this is invalid.
• For \(2 \cdot 3 \cdot 41 \cdot 123\): 123 is not prime, and this has redundant factors, invalid.
• For \(6 \cdot 41\): 6 is not prime (6 = 2×3), invalid.
• For \(2 \cdot 3 \cdot 41\): 2, 3, and 41 are all prime numbers. Also, \(2 \times 3 \times 41 = 246\), so this works.

Answer:

\(2 \cdot 3 \cdot 41\) (the option with \(2 \cdot 3 \cdot 41\))