Greatest Common Divisor (GCD) of 122 and 70
The greatest common divisor (GCD) of 122 and 70 is 2.
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 122 and 70?
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 | 122 ÷ 70 = 1 remainder 52 |
| 2 | 70 ÷ 52 = 1 remainder 18 |
| 3 | 52 ÷ 18 = 2 remainder 16 |
| 4 | 18 ÷ 16 = 1 remainder 2 |
| 5 | 16 ÷ 2 = 8 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 151 and 53 | 1 |
| 135 and 90 | 45 |
| 154 and 149 | 1 |
| 40 and 90 | 10 |
| 70 and 22 | 2 |