What is the prime factorization of 115?
Understand the Problem
The question is asking for the prime factorization of the number 115, which involves breaking it down into its prime factors.
Answer
The prime factorization of 115 is $5 \times 23$.
Answer for screen readers
The prime factorization of 115 is $5 \times 23$.
Steps to Solve
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Identify the smallest prime factor Start by dividing 115 by the smallest prime number, which is 2. Since 115 is odd, it isn't divisible by 2. Move to the next prime number, which is 3.
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Check divisibility by 3 Calculate $1 + 1 + 5 = 7$. Since 7 is not divisible by 3, move to the next prime number, which is 5.
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Divide by 5 Divide 115 by 5:
$$ 115 \div 5 = 23 $$
So, 5 is a prime factor, and we're left with 23.
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Check if 23 is prime Next, check if 23 is a prime number. The prime numbers less than the square root of 23 (about 4.8) are 2 and 3. Since 23 is not divisible by either, it is confirmed to be prime.
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Conclude the prime factorization The prime factorization of 115 can now be represented as:
$$ 115 = 5 \times 23 $$
The prime factorization of 115 is $5 \times 23$.
More Information
Prime factorization is a way of expressing a number as the product of its prime factors. It can be useful in various areas of mathematics, including number theory, and helps in understanding the building blocks of numbers.
Tips
- Forgetting to check if a quotient after dividing is prime itself.
- Assuming composites are primes when they are not; always double-check with the prime numbers.
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