Greatest Common Divisor (GCD) of 160 and 196
The greatest common divisor (GCD) of 160 and 196 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 160 and 196?
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 | 160 ÷ 196 = 0 remainder 160 |
| 2 | 196 ÷ 160 = 1 remainder 36 |
| 3 | 160 ÷ 36 = 4 remainder 16 |
| 4 | 36 ÷ 16 = 2 remainder 4 |
| 5 | 16 ÷ 4 = 4 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 145 and 172 | 1 |
| 187 and 103 | 1 |
| 180 and 148 | 4 |
| 88 and 124 | 4 |
| 136 and 17 | 17 |