What are the prime factors of 61?
Understand the Problem
The question is asking for the prime factors of the number 61, which means we need to identify which prime numbers multiply together to give the original number.
Answer
61
Answer for screen readers
The prime factor of 61 is 61
Steps to Solve
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Check if 61 is a prime number
A prime number is a number greater than 1 that has no divisors other than 1 and itself. To determine if 61 is a prime number, we need to check if it is divisible by any prime number less than or equal to $\sqrt{61}$. The square root of 61 is approximately 7.8, so we only need to check divisibility by the prime numbers less than or equal to 7 (which are 2, 3, 5, and 7).
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Test divisibility by 2
61 is not an even number, so it is not divisible by 2.
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Test divisibility by 3
To test divisibility by 3, sum the digits of 61: $6 + 1 = 7$. Since 7 is not divisible by 3, 61 is also not divisible by 3.
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Test divisibility by 5
Numbers divisible by 5 end in 0 or 5. Since 61 does not end in 0 or 5, it is not divisible by 5.
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Test divisibility by 7
Use the divisibility rule for 7: double the last digit of 61 (which is 1) to get 2, then subtract this from the remaining leading part of the number (which is 6). Thus, $6 - 2 = 4$. Since 4 is not divisible by 7, 61 is not divisible by 7.
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Conclusion
Since 61 is not divisible by any of these primes, 61 is itself a prime number, and hence the only prime factor of 61 is 61 itself.
The prime factor of 61 is 61
More Information
A fun fact is that 61 is both a prime number and a prime factor. Meaning it only has itself and 1 as its divisors.
Tips
A common mistake is to not test all prime numbers up to the square root of the given number. Always ensure to check divisibility by all primes up to $\sqrt{n}$.
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