What is GCD(9, 61)?

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 61 is 1.

How to compute GCD(9, 61)

Comparing the divisors of 9 and 61

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 61:

1, 61

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 61 by 9. The quotient is 6 and the remainder is 7.
  2. The previous divisor (9) is now the dividend. The remainder (7) is the new divisor. Divide 9 by 7. The quotient is 1 and the remainder is 2.
  3. The previous divisor (7) is now the dividend. The remainder (2) is the new divisor. Divide 7 by 2. The quotient is 3 and the remainder is 1.
  4. The previous divisor (2) is now the dividend. The remainder (1) is the new divisor. Divide 2 by 1. The quotient is 2 and the remainder is 0.
  5. When you reach a remainder of 0, the last divisor (in this case, 1) is the GCD.