What is GCD(7, 14)?

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

The GCD of 7 and 14 is 7.

How to compute GCD(7, 14)

Comparing the divisors of 7 and 14

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

Divisors of 7:

1, 7

Divisors of 14:

1, 2, 7, 14

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