Greatest Common Divisor (GCD) of 103 and 152
The greatest common divisor (GCD) of 103 and 152 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 152?
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 ÷ 152 = 0 remainder 103 |
| 2 | 152 ÷ 103 = 1 remainder 49 |
| 3 | 103 ÷ 49 = 2 remainder 5 |
| 4 | 49 ÷ 5 = 9 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 178 and 37 | 1 |
| 172 and 138 | 2 |
| 97 and 182 | 1 |
| 122 and 86 | 2 |
| 145 and 123 | 1 |