Greatest Common Divisor (GCD) of 196 and 144
The greatest common divisor (GCD) of 196 and 144 is 4.
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 196 and 144?
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 | 196 ÷ 144 = 1 remainder 52 |
| 2 | 144 ÷ 52 = 2 remainder 40 |
| 3 | 52 ÷ 40 = 1 remainder 12 |
| 4 | 40 ÷ 12 = 3 remainder 4 |
| 5 | 12 ÷ 4 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 95 and 105 | 5 |
| 66 and 121 | 11 |
| 117 and 194 | 1 |
| 100 and 36 | 4 |
| 91 and 10 | 1 |