Greatest Common Divisor (GCD) of 66 and 103
The greatest common divisor (GCD) of 66 and 103 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 66 and 103?
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 | 66 ÷ 103 = 0 remainder 66 |
| 2 | 103 ÷ 66 = 1 remainder 37 |
| 3 | 66 ÷ 37 = 1 remainder 29 |
| 4 | 37 ÷ 29 = 1 remainder 8 |
| 5 | 29 ÷ 8 = 3 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 188 and 152 | 4 |
| 124 and 155 | 31 |
| 134 and 130 | 2 |
| 54 and 137 | 1 |
| 44 and 176 | 44 |