Greatest Common Divisor (GCD) of 49 and 85
The greatest common divisor (GCD) of 49 and 85 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 49 and 85?
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 | 49 ÷ 85 = 0 remainder 49 |
| 2 | 85 ÷ 49 = 1 remainder 36 |
| 3 | 49 ÷ 36 = 1 remainder 13 |
| 4 | 36 ÷ 13 = 2 remainder 10 |
| 5 | 13 ÷ 10 = 1 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 106 and 44 | 2 |
| 47 and 34 | 1 |
| 145 and 162 | 1 |
| 122 and 137 | 1 |
| 180 and 120 | 60 |