What is GCD(84, 5)?

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 5 is 1.

How to compute GCD(84, 5)

Comparing the divisors of 84 and 5

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 5:

1, 5

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 84 by 5. The quotient is 16 and the remainder is 4.
  2. The previous divisor (5) is now the dividend. The remainder (4) is the new divisor. Divide 5 by 4. The quotient is 1 and the remainder is 1.
  3. The previous divisor (4) is now the dividend. The remainder (1) is the new divisor. Divide 4 by 1. The quotient is 4 and the remainder is 0.
  4. When you reach a remainder of 0, the last divisor (in this case, 1) is the GCD.