Write the prime factorization of 42
Understand the Problem
The question is asking for the prime factorization of the number 42, which involves determining the prime numbers that multiply together to give 42.
Answer
The prime factorization of 42 is $2 \times 3 \times 7$.
Answer for screen readers
The prime factorization of 42 is $2 \times 3 \times 7$.
Steps to Solve
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Start with the number We begin by examining the number 42 to find its smallest prime factor.
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Check divisibility by the smallest prime (2) Since 42 is even, it is divisible by 2. We can divide: $$ 42 \div 2 = 21 $$
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Factor the resulting number (21) Now we look at 21. Next, we check if it can be divided by the next smallest prime, which is 3. $$ 21 \div 3 = 7 $$
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Identify if the last number (7) is prime The last number we have is 7, which is itself a prime number. Thus, it cannot be factored further.
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Write the prime factorization We compile the prime factors we found. The prime factorization of 42 can be expressed as: $$ 42 = 2 \times 3 \times 7 $$
The prime factorization of 42 is $2 \times 3 \times 7$.
More Information
Prime factorization is useful for various applications in math such as finding the greatest common divisor or least common multiple. Each number can be uniquely factored into primes, which is a fundamental principle in number theory.
Tips
- Forgetting to check divisibility by all necessary primes.
- Stopping the factorization too early; always ensure the last number is prime.
