Is 97 a prime or composite number?
Understand the Problem
The question is asking us to determine whether the number 97 is a prime number, which means it has no divisors other than 1 and itself, or a composite number, which has divisors other than 1 and itself. To solve this, we will check if 97 can be divided evenly by any number other than 1 and 97.
Answer
Prime
Answer for screen readers
97 is a prime number
Steps to Solve
- Identify the range of potential divisors
To determine if a number is prime, check possible divisors up to its square root. For 97, the square root is approximately 9.8, so we need to check divisors up to 9.
- Test for divisibility
Check if 97 is divisible by any prime numbers less than or equal to 9 (2, 3, 5, 7).
- Check divisibility by 2
97 is not an even number, so it is not divisible by 2.
- Check divisibility by 3
Sum the digits of 97: $9 + 7 = 16$. Since 16 is not divisible by 3, 97 is not divisible by 3.
- Check divisibility by 5
97 does not end in 0 or 5, so it is not divisible by 5.
- Check divisibility by 7
Dividing 97 by 7 gives approximately 13.857, which is not an integer, so 97 is not divisible by 7.
- Conclude that 97 is prime
Since 97 is not divisible by any of these prime numbers, it has no divisors other than 1 and itself.
97 is a prime number
More Information
Prime numbers are fundamental in number theory because they are the building blocks of all natural numbers—every number is either a prime or can be factored into primes.
Tips
A common mistake when checking if a number is prime is not checking divisibility up to the square root and missing potential factors. Always ensure you check up to the square root of the number.
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