Number Classification: Is 29 Prime or Composite?

To determine whether the number $n = 29$ is prime or composite, we will check if $n$ has any divisors other than 1 and itself.

The definition of a prime number is one that has exactly two distinct positive divisors: 1 and itself. Conversely, a composite number has more than two distinct positive divisors.

First, observe that the square root of 29 is approximately 5.385. This tells us that we only need to check divisibility by all prime numbers less than or equal to 5. These primes are 2, 3, and 5.

• Check divisibility by 2: 29 is odd, so it is not divisible by 2.
• Check divisibility by 3: The sum of the digits of 29 is $2 + 9 = 11$, which is not divisible by 3, so 29 is not divisible by 3.
• Check divisibility by 5: 29 does not end in 0 or 5, so it is not divisible by 5.

Since 29 is not divisible by any of these primes, it has no divisors other than 1 and 29 itself. Therefore, 29 is a prime number.

Hence, the solution to the problem is that the number $n = 29$ is Prime.