Prime factor 42
Understand the Problem
The question is asking for the prime factorization of the number 42, which means we need to break it down into the prime numbers that multiply together to give 42.
Answer
2 \times 3 \times 7
Answer for screen readers
The final answer is 2 \times 3 \times 7
Steps to Solve
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Start with the smallest prime number
Divide 42 by the smallest prime number, which is 2. $$ 42 \div 2 = 21 $$
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Factor the quotient
Continue factoring the quotient, in this case 21, by the smallest prime number. Since 21 is not divisible by 2, try the next smallest prime number, which is 3. $$ 21 \div 3 = 7 $$
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Check for further factorization
The quotient 7 is a prime number, so it cannot be factored further. Thus, the prime factorization of 42 is complete.
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Write the final prime factorization
Combine all the prime factors found. $$ 42 = 2 \times 3 \times 7 $$
The final answer is 2 \times 3 \times 7
More Information
Prime factorization is useful in various areas of mathematics, including simplifying fractions, finding the greatest common divisor (GCD), and the least common multiple (LCM).
Tips
A common mistake is not starting with the smallest prime number or skipping primes. Always start with 2, then move to 3, 5, and so on.
