One consequence of this theorem is that when forming the prime factorization of a number n, we need only consider prime numbers less than or equal to the square root of n.
For example, if you search for the prime factors of 101, you need only try dividing 101 by primes up to sqrt(101); the largest of these is 7. Since 2, 3, 5, and 7 are not factors of 101, we can safely conclude that 101 is prime.