Greatest Common Divisor (GCD) of 107 and 145
The greatest common divisor (GCD) of 107 and 145 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 107 and 145?
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 | 107 ÷ 145 = 0 remainder 107 |
| 2 | 145 ÷ 107 = 1 remainder 38 |
| 3 | 107 ÷ 38 = 2 remainder 31 |
| 4 | 38 ÷ 31 = 1 remainder 7 |
| 5 | 31 ÷ 7 = 4 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 121 and 112 | 1 |
| 72 and 113 | 1 |
| 117 and 22 | 1 |
| 35 and 123 | 1 |
| 161 and 74 | 1 |