Greatest Common Divisor (GCD) of 70 and 165
The greatest common divisor (GCD) of 70 and 165 is 5.
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 70 and 165?
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 | 70 ÷ 165 = 0 remainder 70 |
| 2 | 165 ÷ 70 = 2 remainder 25 |
| 3 | 70 ÷ 25 = 2 remainder 20 |
| 4 | 25 ÷ 20 = 1 remainder 5 |
| 5 | 20 ÷ 5 = 4 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 190 and 95 | 95 |
| 188 and 71 | 1 |
| 153 and 119 | 17 |
| 72 and 89 | 1 |
| 123 and 161 | 1 |