What is GCD(9, 72)?

The GCD (Greatest Common Divisor) is the largest number that can divide two (or more) numbers without leaving a remainder.

The GCD of 9 and 72 is 9.

How to compute GCD(9, 72)

Comparing the divisors of 9 and 72

This first method consists in listing the divisors of the two numbers and then identifying the largest one they have in common.

Divisors of 9:

1, 3, 9

Divisors of 72:

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

We can see from these two lists that the greatest divisor they have in common is: 9

For small numbers, this can be done quickly. However, as numbers increase, the list of potential divisors grows longer, making this method cumbersome and less practical.

Euclid's algorithm

Fortunately, there's a much more efficient method: Euclid's algorithm. It's particularly well-suited to larger numbers. Here's how it works:

  1. Divide 72 by 9. The quotient is 8 and the remainder is 0.
  2. When you reach a remainder of 0, the last divisor (in this case, 9) is the GCD.