Greatest Common Divisor (GCD) of 192 and 153
The greatest common divisor (GCD) of 192 and 153 is 3.
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 192 and 153?
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 | 192 ÷ 153 = 1 remainder 39 |
| 2 | 153 ÷ 39 = 3 remainder 36 |
| 3 | 39 ÷ 36 = 1 remainder 3 |
| 4 | 36 ÷ 3 = 12 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 185 and 86 | 1 |
| 198 and 198 | 198 |
| 196 and 72 | 4 |
| 188 and 165 | 1 |
| 141 and 118 | 1 |