Greatest Common Divisor (GCD) of 40 and 59
The greatest common divisor (GCD) of 40 and 59 is 1.
What is the Greatest Common Divisor (GCD)?
The GCD of two integers is the largest positive integer that divides both numbers without leaving a remainder. It is useful in simplifying fractions, finding common factors, and in number theory.
How to Calculate the GCD of 40 and 59?
We use the Euclidean algorithm, which involves the following steps:
- Divide the larger number by the smaller number.
- Replace the larger number with the smaller number and the smaller number with the remainder from the division.
- Repeat this process until the remainder is zero.
- The non-zero remainder just before zero is the GCD.
Step-by-Step Euclidean Algorithm
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 59 = 0 remainder 40 |
| 2 | 59 ÷ 40 = 1 remainder 19 |
| 3 | 40 ÷ 19 = 2 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 121 and 38 | 1 |
| 110 and 192 | 2 |
| 14 and 68 | 2 |
| 173 and 28 | 1 |
| 44 and 84 | 4 |