Greatest Common Divisor (GCD) of 62 and 104
The greatest common divisor (GCD) of 62 and 104 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 62 and 104?
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 | 62 ÷ 104 = 0 remainder 62 |
| 2 | 104 ÷ 62 = 1 remainder 42 |
| 3 | 62 ÷ 42 = 1 remainder 20 |
| 4 | 42 ÷ 20 = 2 remainder 2 |
| 5 | 20 ÷ 2 = 10 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 188 and 84 | 4 |
| 71 and 97 | 1 |
| 91 and 20 | 1 |
| 11 and 169 | 1 |
| 185 and 108 | 1 |