Greatest Common Divisor (GCD) of 99 and 164
The greatest common divisor (GCD) of 99 and 164 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 99 and 164?
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 | 99 ÷ 164 = 0 remainder 99 |
| 2 | 164 ÷ 99 = 1 remainder 65 |
| 3 | 99 ÷ 65 = 1 remainder 34 |
| 4 | 65 ÷ 34 = 1 remainder 31 |
| 5 | 34 ÷ 31 = 1 remainder 3 |
| 6 | 31 ÷ 3 = 10 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 69 and 138 | 69 |
| 175 and 188 | 1 |
| 145 and 23 | 1 |
| 104 and 52 | 52 |
| 56 and 181 | 1 |