What is GCD(91, 5)?
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 5 is 1.
How to compute GCD(91, 5)
Comparing the divisors of 91 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 91:
1, 7, 13, 91
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:
- Divide 91 by 5. The quotient is 18 and the remainder is 1.
- The previous divisor (5) is now the dividend. The remainder (1) is the new divisor. Divide 5 by 1. The quotient is 5 and the remainder is 0.
- When you reach a remainder of 0, the last divisor (in this case, 1) is the GCD.