Greatest Common Divisor (GCD) of 152 and 185
The greatest common divisor (GCD) of 152 and 185 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 152 and 185?
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 | 152 ÷ 185 = 0 remainder 152 |
| 2 | 185 ÷ 152 = 1 remainder 33 |
| 3 | 152 ÷ 33 = 4 remainder 20 |
| 4 | 33 ÷ 20 = 1 remainder 13 |
| 5 | 20 ÷ 13 = 1 remainder 7 |
| 6 | 13 ÷ 7 = 1 remainder 6 |
| 7 | 7 ÷ 6 = 1 remainder 1 |
| 8 | 6 ÷ 1 = 6 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 158 and 173 | 1 |
| 180 and 99 | 9 |
| 62 and 74 | 2 |
| 196 and 188 | 4 |
| 61 and 33 | 1 |