97 is a prime number. A prime number is defined as a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. This means that a prime number has exactly two distinct positive divisors: 1 and itself.
In the case of 97, its only divisors are 1 and 97. There are no other numbers that can divide 97 evenly without leaving a remainder. To determine if a number is prime, you can check for divisibility by all prime numbers less than or equal to the square root of that number. The square root of 97 is approximately 9.8, so we only need to consider the prime numbers less than or equal to 9, which are 2, 3, 5, and 7.
– 97 is odd, so it’s not divisible by 2.
– The sum of the digits of 97 (which is 9 + 7 = 16) is not divisible by 3, so 97 is not divisible by 3.
– 97 does not end in 0 or 5, so it’s not divisible by 5.
– Finally, dividing 97 by 7 gives approximately 13.857, which is not an integer.
Since 97 is not divisible by any of these primes, we can conclude that 97 is indeed a prime number.