Greatest Common Divisor (GCD) of 98 and 169
The greatest common divisor (GCD) of 98 and 169 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 98 and 169?
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 | 98 ÷ 169 = 0 remainder 98 |
| 2 | 169 ÷ 98 = 1 remainder 71 |
| 3 | 98 ÷ 71 = 1 remainder 27 |
| 4 | 71 ÷ 27 = 2 remainder 17 |
| 5 | 27 ÷ 17 = 1 remainder 10 |
| 6 | 17 ÷ 10 = 1 remainder 7 |
| 7 | 10 ÷ 7 = 1 remainder 3 |
| 8 | 7 ÷ 3 = 2 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 149 and 62 | 1 |
| 165 and 137 | 1 |
| 53 and 139 | 1 |
| 151 and 14 | 1 |
| 188 and 20 | 4 |