Greatest Common Divisor (GCD) of 147 and 189
The greatest common divisor (GCD) of 147 and 189 is 21.
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 147 and 189?
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 | 147 ÷ 189 = 0 remainder 147 |
| 2 | 189 ÷ 147 = 1 remainder 42 |
| 3 | 147 ÷ 42 = 3 remainder 21 |
| 4 | 42 ÷ 21 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 97 and 29 | 1 |
| 73 and 114 | 1 |
| 194 and 146 | 2 |
| 45 and 124 | 1 |
| 10 and 16 | 2 |