Greatest Common Divisor (GCD) of 24 and 36
The greatest common divisor (GCD) of 24 and 36 is 12.
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 24 and 36?
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 | 24 ÷ 36 = 0 remainder 24 |
| 2 | 36 ÷ 24 = 1 remainder 12 |
| 3 | 24 ÷ 12 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 161 and 10 | 1 |
| 167 and 100 | 1 |
| 128 and 140 | 4 |
| 21 and 198 | 3 |
| 17 and 127 | 1 |