What is the prime factorization of 41?
Understand the Problem
The question is asking for the prime factorization of the number 41. Since 41 is a prime number, its only factors are 1 and 41 itself.
Answer
The prime factorization of 41 is $41^1$.
Answer for screen readers
The prime factorization of 41 is $41^1$.
Steps to Solve
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Identify Prime Number Status Since we are looking at the number 41, we first need to confirm whether it is a prime number or not. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
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Check for Divisibility Next, we check if 41 can be divided by any prime numbers less than or equal to its square root. The square root of 41 is approximately 6.4, so we check the prime numbers 2, 3, 5.
- Checking divisibility by 2: 41 is odd, so it is not divisible by 2.
- Checking divisibility by 3: The sum of the digits of 41 is 4 + 1 = 5, which is not divisible by 3.
- Checking divisibility by 5: 41 does not end in 0 or 5, so it is not divisible by 5.
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Conclusion About Prime Status Since 41 is not divisible by any prime number up to 6.4, we conclude that it is a prime number.
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Present Prime Factorization The prime factorization of a prime number is the number itself. Thus, we write the prime factorization of 41 as: $$ 41 = 41^1 $$
The prime factorization of 41 is $41^1$.
More Information
41 is the 13th prime number and is often recognized for its role in various mathematical contexts. It is also a prime number in the decimal system.
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