Greatest Common Divisor (GCD) of 101 and 170
The greatest common divisor (GCD) of 101 and 170 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 101 and 170?
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 | 101 ÷ 170 = 0 remainder 101 |
| 2 | 170 ÷ 101 = 1 remainder 69 |
| 3 | 101 ÷ 69 = 1 remainder 32 |
| 4 | 69 ÷ 32 = 2 remainder 5 |
| 5 | 32 ÷ 5 = 6 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 100 and 98 | 2 |
| 59 and 138 | 1 |
| 65 and 61 | 1 |
| 103 and 122 | 1 |
| 88 and 94 | 2 |