
Greatest Common Divisor (GCD) of 36 and 109
The greatest common divisor (GCD) of 36 and 109 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 36 and 109?
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 | 36 ÷ 109 = 0 remainder 36 |
2 | 109 ÷ 36 = 3 remainder 1 |
3 | 36 ÷ 1 = 36 remainder 0 |
Examples of GCD Calculations
Numbers | GCD |
---|---|
138 and 174 | 6 |
82 and 83 | 1 |
93 and 150 | 3 |
199 and 72 | 1 |
91 and 18 | 1 |