Greatest Common Divisor (GCD) of 88 and 152
The greatest common divisor (GCD) of 88 and 152 is 8.
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 88 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 | 88 ÷ 152 = 0 remainder 88 |
| 2 | 152 ÷ 88 = 1 remainder 64 |
| 3 | 88 ÷ 64 = 1 remainder 24 |
| 4 | 64 ÷ 24 = 2 remainder 16 |
| 5 | 24 ÷ 16 = 1 remainder 8 |
| 6 | 16 ÷ 8 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 162 and 89 | 1 |
| 184 and 184 | 184 |
| 129 and 113 | 1 |
| 122 and 178 | 2 |
| 31 and 138 | 1 |