What is GCD(9, 31)?

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 31 is 1.

How to compute GCD(9, 31)

Comparing the divisors of 9 and 31

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 31:

1, 31

We can see from these two lists that the greatest divisor they have in common is: 1

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 31 by 9. The quotient is 3 and the remainder is 4.
  2. The previous divisor (9) is now the dividend. The remainder (4) is the new divisor. Divide 9 by 4. The quotient is 2 and the remainder is 1.
  3. The previous divisor (4) is now the dividend. The remainder (1) is the new divisor. Divide 4 by 1. The quotient is 4 and the remainder is 0.
  4. When you reach a remainder of 0, the last divisor (in this case, 1) is the GCD.