What is GCD(6, 16)?

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

The GCD of 6 and 16 is 2.

How to compute GCD(6, 16)

Comparing the divisors of 6 and 16

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

Divisors of 6:

1, 2, 3, 6

Divisors of 16:

1, 2, 4, 8, 16

We can see from these two lists that the greatest divisor they have in common is: 2

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