What is GCD(18, 9)?
The GCD (Greatest Common Divisor) is the largest number that can divide two (or more) numbers without leaving a remainder.
The GCD of 18 and 9 is 9.
How to compute GCD(18, 9)
Comparing the divisors of 18 and 9
This first method consists in listing the divisors of the two numbers and then identifying the largest one they have in common.
Divisors of 18:
1, 2, 3, 6, 9, 18
Divisors of 9:
1, 3, 9
We can see from these two lists that the greatest divisor they have in common is: 9
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 18 by 9. The quotient is 2 and the remainder is 0.
- When you reach a remainder of 0, the last divisor (in this case, 9) is the GCD.