What is GCD(91, 8)?

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

The GCD of 91 and 8 is 1.

How to compute GCD(91, 8)

Comparing the divisors of 91 and 8

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

Divisors of 91:

1, 7, 13, 91

Divisors of 8:

1, 2, 4, 8

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 91 by 8. The quotient is 11 and the remainder is 3.
  2. The previous divisor (8) is now the dividend. The remainder (3) is the new divisor. Divide 8 by 3. The quotient is 2 and the remainder is 2.
  3. The previous divisor (3) is now the dividend. The remainder (2) is the new divisor. Divide 3 by 2. The quotient is 1 and the remainder is 1.
  4. The previous divisor (2) is now the dividend. The remainder (1) is the new divisor. Divide 2 by 1. The quotient is 2 and the remainder is 0.
  5. When you reach a remainder of 0, the last divisor (in this case, 1) is the GCD.