What is GCD(92, 8)?
The GCD (Greatest Common Divisor) is the largest number that can divide two (or more) numbers without leaving a remainder.
The GCD of 92 and 8 is 4.
How to compute GCD(92, 8)
Comparing the divisors of 92 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 92:
1, 2, 4, 23, 46, 92
Divisors of 8:
1, 2, 4, 8
We can see from these two lists that the greatest divisor they have in common is: 4
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 92 by 8. The quotient is 11 and the remainder is 4.
- The previous divisor (8) is now the dividend. The remainder (4) is the new divisor. Divide 8 by 4. The quotient is 2 and the remainder is 0.
- When you reach a remainder of 0, the last divisor (in this case, 4) is the GCD.