53 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. To determine whether 53 is prime, we can check for divisibility by prime numbers that are less than or equal to the square root of 53.
The square root of 53 is approximately 7.28, so we only need to test the prime numbers 2, 3, 5, and 7. Let’s examine each:
- 53 is odd, so it is not divisible by 2.
- The sum of the digits in 53 is 8 (5 + 3), which is not divisible by 3, so 53 is not divisible by 3.
- 53 does not end in 0 or 5, so it cannot be divisible by 5.
- Finally, dividing 53 by 7 gives approximately 7.57, which indicates it is also not divisible by 7.
Since 53 is not divisible by any of these prime numbers, we conclude that it has no divisors other than 1 and itself. Therefore, 53 is indeed a prime number.