89 is a prime number. A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. In the case of 89, the only divisors are 1 and 89.
To determine whether 89 is prime or composite, we can check for divisibility by all prime numbers less than or equal to the square root of 89. The square root of 89 is approximately 9.43. Therefore, we only need to consider the prime numbers up to 9, which are 2, 3, 5, and 7.
– 89 is not even, so it is not divisible by 2.
– The sum of the digits of 89 (8 + 9 = 17) is not divisible by 3, so 89 is not divisible by 3.
– 89 does not end in 0 or 5, meaning it is not divisible by 5.
– Finally, when we divide 89 by 7, we get approximately 12.71, which is not a whole number, indicating that 89 is not divisible by 7.
Since 89 is not divisible by any of these prime numbers, we conclude that 89 is indeed a prime number.