
Greatest Common Divisor (GCD) of 64 and 157
The greatest common divisor (GCD) of 64 and 157 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 64 and 157?
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 | 64 ÷ 157 = 0 remainder 64 |
2 | 157 ÷ 64 = 2 remainder 29 |
3 | 64 ÷ 29 = 2 remainder 6 |
4 | 29 ÷ 6 = 4 remainder 5 |
5 | 6 ÷ 5 = 1 remainder 1 |
6 | 5 ÷ 1 = 5 remainder 0 |
Examples of GCD Calculations
Numbers | GCD |
---|---|
182 and 174 | 2 |
107 and 63 | 1 |
27 and 94 | 1 |
70 and 109 | 1 |
26 and 16 | 2 |