Greatest Common Divisor (GCD) of 64 and 101
The greatest common divisor (GCD) of 64 and 101 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 101?
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 ÷ 101 = 0 remainder 64 |
| 2 | 101 ÷ 64 = 1 remainder 37 |
| 3 | 64 ÷ 37 = 1 remainder 27 |
| 4 | 37 ÷ 27 = 1 remainder 10 |
| 5 | 27 ÷ 10 = 2 remainder 7 |
| 6 | 10 ÷ 7 = 1 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 133 and 151 | 1 |
| 71 and 87 | 1 |
| 158 and 149 | 1 |
| 140 and 152 | 4 |
| 53 and 85 | 1 |