What is GCD(84, 7)?

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 7 is 7.

How to compute GCD(84, 7)

Comparing the divisors of 84 and 7

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 7:

1, 7

We can see from these two lists that the greatest divisor they have in common is: 7

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 7. The quotient is 12 and the remainder is 0.
  2. When you reach a remainder of 0, the last divisor (in this case, 7) is the GCD.