What is GCD(44, 6)?
The GCD (Greatest Common Divisor) is the largest number that can divide two (or more) numbers without leaving a remainder.
The GCD of 44 and 6 is 2.
How to compute GCD(44, 6)
Comparing the divisors of 44 and 6
This first method consists in listing the divisors of the two numbers and then identifying the largest one they have in common.
Divisors of 44:
1, 2, 4, 11, 22, 44
Divisors of 6:
1, 2, 3, 6
We can see from these two lists that the greatest divisor they have in common is: 2
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 44 by 6. The quotient is 7 and the remainder is 2.
- The previous divisor (6) is now the dividend. The remainder (2) is the new divisor. Divide 6 by 2. The quotient is 3 and the remainder is 0.
- When you reach a remainder of 0, the last divisor (in this case, 2) is the GCD.