Greatest Common Divisor (GCD) of 174 and 99
The greatest common divisor (GCD) of 174 and 99 is 3.
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 174 and 99?
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 | 174 ÷ 99 = 1 remainder 75 |
| 2 | 99 ÷ 75 = 1 remainder 24 |
| 3 | 75 ÷ 24 = 3 remainder 3 |
| 4 | 24 ÷ 3 = 8 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 169 and 145 | 1 |
| 103 and 107 | 1 |
| 152 and 114 | 38 |
| 157 and 67 | 1 |
| 85 and 57 | 1 |