
Greatest Common Divisor (GCD) of 47 and 165
The greatest common divisor (GCD) of 47 and 165 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 47 and 165?
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 | 47 ÷ 165 = 0 remainder 47 |
2 | 165 ÷ 47 = 3 remainder 24 |
3 | 47 ÷ 24 = 1 remainder 23 |
4 | 24 ÷ 23 = 1 remainder 1 |
5 | 23 ÷ 1 = 23 remainder 0 |
Examples of GCD Calculations
Numbers | GCD |
---|---|
126 and 49 | 7 |
195 and 122 | 1 |
13 and 58 | 1 |
132 and 59 | 1 |
102 and 146 | 2 |