What is the prime factorization of 47?
Understand the Problem
The question is asking for the prime factorization of the number 47, which means we need to determine the prime numbers that, when multiplied together, equal 47. Since 47 is a prime number itself, its only prime factor is 47.
Answer
47
Answer for screen readers
The prime factorization of 47 is 47
Steps to Solve
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Check if 47 is a prime number
A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. To determine if 47 is prime, we test if it can be divided evenly by any prime numbers less than or equal to its square root (approximately 6.86).
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Test divisibility by prime numbers up to the square root
Check if 47 is divisible by 2, 3, and 5 (primes less than or equal to the square root of 47):
- 47 is odd, so it is not divisible by 2.
- The sum of the digits of 47 is 4+7=11, which is not divisible by 3, so 47 is not divisible by 3.
- 47 does not end in 0 or 5, so it is not divisible by 5. Since 47 is not divisible by any of these primes, it is a prime number.
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Conclude the prime factorization
Since 47 is a prime number, the prime factorization of 47 is simply 47 itself.
The prime factorization of 47 is 47
More Information
47 is a prime number, which means it is only divisible by 1 and itself. Therefore, its only prime factor is 47.
Tips
A common mistake is to forget that prime numbers only have two factors (1 and themselves). Double-check divisibility using prime numbers up to the square root of the number.
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