Greatest Common Divisor (GCD) of 93 and 162
The greatest common divisor (GCD) of 93 and 162 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 93 and 162?
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 | 93 ÷ 162 = 0 remainder 93 |
| 2 | 162 ÷ 93 = 1 remainder 69 |
| 3 | 93 ÷ 69 = 1 remainder 24 |
| 4 | 69 ÷ 24 = 2 remainder 21 |
| 5 | 24 ÷ 21 = 1 remainder 3 |
| 6 | 21 ÷ 3 = 7 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 110 and 138 | 2 |
| 150 and 77 | 1 |
| 126 and 123 | 3 |
| 145 and 144 | 1 |
| 174 and 108 | 6 |