What is GCD(9, 21)?

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 21 is 3.

How to compute GCD(9, 21)

Comparing the divisors of 9 and 21

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 21:

1, 3, 7, 21

We can see from these two lists that the greatest divisor they have in common is: 3

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 21 by 9. The quotient is 2 and the remainder is 3.
  2. The previous divisor (9) is now the dividend. The remainder (3) is the new divisor. Divide 9 by 3. The quotient is 3 and the remainder is 0.
  3. When you reach a remainder of 0, the last divisor (in this case, 3) is the GCD.