What is GCD(8, 24)?
The GCD (Greatest Common Divisor) is the largest number that can divide two (or more) numbers without leaving a remainder.
The GCD of 8 and 24 is 8.
How to compute GCD(8, 24)
Comparing the divisors of 8 and 24
This first method consists in listing the divisors of the two numbers and then identifying the largest one they have in common.
Divisors of 8:
1, 2, 4, 8
Divisors of 24:
1, 2, 3, 4, 6, 8, 12, 24
We can see from these two lists that the greatest divisor they have in common is: 8
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 24 by 8. The quotient is 3 and the remainder is 0.
- When you reach a remainder of 0, the last divisor (in this case, 8) is the GCD.