
Greatest Common Divisor (GCD) of 147 and 82
The greatest common divisor (GCD) of 147 and 82 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 147 and 82?
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 | 147 ÷ 82 = 1 remainder 65 |
2 | 82 ÷ 65 = 1 remainder 17 |
3 | 65 ÷ 17 = 3 remainder 14 |
4 | 17 ÷ 14 = 1 remainder 3 |
5 | 14 ÷ 3 = 4 remainder 2 |
6 | 3 ÷ 2 = 1 remainder 1 |
7 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
Numbers | GCD |
---|---|
134 and 111 | 1 |
82 and 41 | 41 |
141 and 50 | 1 |
49 and 143 | 1 |
194 and 58 | 2 |