There are just four natural numbers less than 100, which have exactly three factors. One of them is 25, what are the other three? What can be said about these numbers?

A natural number has exactly three factors only if it is the square of a prime number (the factors are 1, the prime, and the square).

For 25 = 5², the factors are 1, 5 and 25.

We look for squares of primes less than 100:

• 2² = 4 (factors: 1, 2, 4) ✓
• 3² = 9 (factors: 1, 3, 9) ✓
• 5² = 25 (factors: 1, 5, 25) ✓ (given)
• 7² = 49 (factors: 1, 7, 49) ✓
• 11² = 121 > 100 ✗

Hence, the other three numbers are 4, 9 and 49. These numbers are squares of prime numbers.