What is GCD(84, 60)?

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

The GCD of 84 and 60 is 12.

How to compute GCD(84, 60)

Comparing the divisors of 84 and 60

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

Divisors of 84:

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Divisors of 60:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

We can see from these two lists that the greatest divisor they have in common is: 12

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 84 by 60. The quotient is 1 and the remainder is 24.
  2. The previous divisor (60) is now the dividend. The remainder (24) is the new divisor. Divide 60 by 24. The quotient is 2 and the remainder is 12.
  3. The previous divisor (24) is now the dividend. The remainder (12) is the new divisor. Divide 24 by 12. The quotient is 2 and the remainder is 0.
  4. When you reach a remainder of 0, the last divisor (in this case, 12) is the GCD.