What is GCD(1, 48)?
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 48 is 1.
How to compute GCD(1, 48)
Comparing the divisors of 1 and 48
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 48:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
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 48 by 1. The quotient is 48 and the remainder is 0.
- When you reach a remainder of 0, the last divisor (in this case, 1) is the GCD.