How divisibility rules can help you find the prime factorization?

Answer 1

Suppose you were trying to find the prime factorization of 123. You know that half of the divisors will be less than the square root. Since the square root is between 11 and 12, you only need to test 2, 3, 5, 7 and 11 as prime factors. If you know the rules of divisibility, you already know that 2 and 5 aren't factors and 3 is. It saves time.

Answer 2

Applying the rules of divisibility, you know that 180 is divisible by 2, 3 and 5. Dividing those into 180 leaves 6, which is another 2 and 3.

2 x 2 x 3 x 3 x 5 = 180