What is GCD(1, 72)?
The GCD (Greatest Common Divisor) is the largest number that can divide two (or more) numbers without leaving a remainder.
The GCD of 1 and 72 is 1.
How to compute GCD(1, 72)
Comparing the divisors of 1 and 72
This first method consists in listing the divisors of the two numbers and then identifying the largest one they have in common.
Divisors of 1:
1
Divisors of 72:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
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 72 by 1. The quotient is 72 and the remainder is 0.
- When you reach a remainder of 0, the last divisor (in this case, 1) is the GCD.