Greatest Common Divisor (GCD) of 89 and 153
The greatest common divisor (GCD) of 89 and 153 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 89 and 153?
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 | 89 ÷ 153 = 0 remainder 89 |
| 2 | 153 ÷ 89 = 1 remainder 64 |
| 3 | 89 ÷ 64 = 1 remainder 25 |
| 4 | 64 ÷ 25 = 2 remainder 14 |
| 5 | 25 ÷ 14 = 1 remainder 11 |
| 6 | 14 ÷ 11 = 1 remainder 3 |
| 7 | 11 ÷ 3 = 3 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 120 and 50 | 10 |
| 91 and 176 | 1 |
| 12 and 104 | 4 |
| 162 and 57 | 3 |
| 164 and 115 | 1 |