What is the prime factorization of 87?
Understand the Problem
The question is asking for the prime factors of the number 87, which means we need to identify the prime numbers that multiply together to give 87.
Answer
The prime factors of 87 are $3$ and $29$.
Answer for screen readers
The prime factors of 87 are $3$ and $29$.
Steps to Solve
- Identify the first step in factorization
To find the prime factors of 87, we start by checking the smallest prime numbers. The smallest prime number is 2. Since 87 is odd, it's not divisible by 2.
- Check divisibility by the next prime, 3
Next, we divide 87 by 3.
$$ 87 \div 3 = 29 $$
Since 3 is a prime number and 29 is also a prime number, we have found two prime factors.
- List the prime factors
The prime factors of 87 can now be listed, which are found from our division.
Thus, the prime factorization of 87 is:
$$ 87 = 3 \times 29 $$
The prime factors of 87 are $3$ and $29$.
More Information
Prime factorization is essential in concepts such as number theory and can help in various applications, including finding the greatest common divisor or least common multiple.
Tips
- Forgetting to check all prime numbers: Some might stop at 3 and not realize they can continue checking larger primes like 5, 7, etc., even if 3 already worked.
- Assuming divisibility too quickly: Ensure that division results in whole numbers before concluding it’s a factor.
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