Greatest Common Divisor (GCD) of 164 and 88
The greatest common divisor (GCD) of 164 and 88 is 4.
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 164 and 88?
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 | 164 ÷ 88 = 1 remainder 76 |
| 2 | 88 ÷ 76 = 1 remainder 12 |
| 3 | 76 ÷ 12 = 6 remainder 4 |
| 4 | 12 ÷ 4 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 107 and 59 | 1 |
| 113 and 71 | 1 |
| 178 and 34 | 2 |
| 116 and 65 | 1 |
| 169 and 142 | 1 |