What are the prime factors of 89?
Understand the Problem
The question is asking for the prime factors of the number 89. Prime factors are the prime numbers that multiply together to give the original number.
Answer
The prime factors of 89 are 89.
Answer for screen readers
The prime factors of 89 are 89.
Steps to Solve
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Identify if the number is prime First, we need to check if 89 is a prime number. A prime number has only two positive divisors: 1 and itself.
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Check divisibility To check if 89 is prime, we can test for divisibility by prime numbers less than the square root of 89. The square root of 89 is approximately 9.43, so we check the prime numbers up to 9: 2, 3, 5, and 7.
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Divisibility by 2 89 is an odd number, so it cannot be divided by 2.
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Divisibility by 3 To check divisibility by 3, we add the digits of 89: $8 + 9 = 17$. Since 17 is not divisible by 3, 89 is not divisible by 3.
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Divisibility by 5 A number is divisible by 5 if it ends in 0 or 5. Since 89 ends in 9, it is not divisible by 5.
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Divisibility by 7 To check divisibility by 7, we divide 89 by 7: $$ 89 \div 7 \approx 12.71 $$ Since this is not an integer, 89 is not divisible by 7.
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Conclusion of primality Since 89 is not divisible by any prime numbers up to its square root, we conclude that 89 is a prime number.
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List the prime factors Since 89 is prime, the only prime factor of 89 is itself.
The prime factors of 89 are 89.
More Information
89 is a unique prime number and does not have any other factors besides itself and 1. In fact, it is the 24th prime number in the series of prime numbers.
Tips
- Confusing composite numbers with prime numbers. Remember that prime numbers have only two distinct positive divisors.
