prime factor of 42
Understand the Problem
The question is asking for the prime factors of the number 42, which involves identifying the prime numbers that multiply together to give 42.
Answer
2, 3, 7
Answer for screen readers
The prime factors of 42 are 2, 3, and 7
Steps to Solve
- Identify the smallest prime number that divides 42
Start with the smallest prime number which is 2. Divide 42 by 2. Since 42 is even, it is divisible by 2.
$$ 42 \div 2 = 21 $$
- Identify the next prime factor of 21
Next, look for the smallest prime number that can divide 21. The number 21 is not divisible by 2 (since it is odd), but it is divisible by 3 (since the sum of its digits, 2 + 1 = 3, is divisible by 3).
$$ 21 \div 3 = 7 $$
- Check if 7 is a prime
Lastly, we need to check if 7 is a prime number. Since 7 is only divisible by 1 and itself, it is a prime number. Thus, 7 is the last prime factor of 42.
- Combine the prime factors
Multiplying all the prime factors together, we get:
$$ 2 \times 3 \times 7 = 42 $$
Hence, the prime factors of 42 are 2, 3, and 7.
The prime factors of 42 are 2, 3, and 7
More Information
Prime factorization involves breaking down a number into the set of prime numbers that multiply together to get the original number. Every whole number greater than 1 has a unique prime factorization.
Tips
A common mistake is to forget checking with the smallest prime number at each step, which ensures you find the correct set of prime factors.
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