Greatest Common Divisor (GCD) of 100 and 170
The greatest common divisor (GCD) of 100 and 170 is 10.
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 100 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 | 100 ÷ 170 = 0 remainder 100 |
| 2 | 170 ÷ 100 = 1 remainder 70 |
| 3 | 100 ÷ 70 = 1 remainder 30 |
| 4 | 70 ÷ 30 = 2 remainder 10 |
| 5 | 30 ÷ 10 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 141 and 91 | 1 |
| 159 and 116 | 1 |
| 112 and 27 | 1 |
| 184 and 170 | 2 |
| 145 and 126 | 1 |