Greatest Common Divisor (GCD) of 72 and 120
The greatest common divisor (GCD) of 72 and 120 is 24.
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 72 and 120?
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 | 72 ÷ 120 = 0 remainder 72 |
| 2 | 120 ÷ 72 = 1 remainder 48 |
| 3 | 72 ÷ 48 = 1 remainder 24 |
| 4 | 48 ÷ 24 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 31 and 86 | 1 |
| 169 and 160 | 1 |
| 174 and 119 | 1 |
| 135 and 88 | 1 |
| 137 and 128 | 1 |