
Greatest Common Divisor (GCD) of 182 and 99
The greatest common divisor (GCD) of 182 and 99 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 182 and 99?
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 | 182 ÷ 99 = 1 remainder 83 |
2 | 99 ÷ 83 = 1 remainder 16 |
3 | 83 ÷ 16 = 5 remainder 3 |
4 | 16 ÷ 3 = 5 remainder 1 |
5 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
Numbers | GCD |
---|---|
162 and 166 | 2 |
138 and 40 | 2 |
75 and 198 | 3 |
141 and 147 | 3 |
76 and 122 | 2 |