Greatest Common Divisor (GCD) of 124 and 167
The greatest common divisor (GCD) of 124 and 167 is 1.
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 124 and 167?
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 | 124 ÷ 167 = 0 remainder 124 |
| 2 | 167 ÷ 124 = 1 remainder 43 |
| 3 | 124 ÷ 43 = 2 remainder 38 |
| 4 | 43 ÷ 38 = 1 remainder 5 |
| 5 | 38 ÷ 5 = 7 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 167 and 157 | 1 |
| 135 and 123 | 3 |
| 97 and 58 | 1 |
| 132 and 176 | 44 |
| 153 and 86 | 1 |