Greatest Common Divisor (GCD) of 103 and 157
The greatest common divisor (GCD) of 103 and 157 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 103 and 157?
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 | 103 ÷ 157 = 0 remainder 103 |
| 2 | 157 ÷ 103 = 1 remainder 54 |
| 3 | 103 ÷ 54 = 1 remainder 49 |
| 4 | 54 ÷ 49 = 1 remainder 5 |
| 5 | 49 ÷ 5 = 9 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 101 and 20 | 1 |
| 151 and 159 | 1 |
| 120 and 133 | 1 |
| 121 and 24 | 1 |
| 29 and 63 | 1 |