Greatest Common Divisor (GCD) of 152 and 178
The greatest common divisor (GCD) of 152 and 178 is 2.
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 178?
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 ÷ 178 = 0 remainder 152 |
| 2 | 178 ÷ 152 = 1 remainder 26 |
| 3 | 152 ÷ 26 = 5 remainder 22 |
| 4 | 26 ÷ 22 = 1 remainder 4 |
| 5 | 22 ÷ 4 = 5 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 76 and 105 | 1 |
| 196 and 163 | 1 |
| 179 and 69 | 1 |
| 151 and 30 | 1 |
| 165 and 134 | 1 |