Greatest Common Divisor (GCD) of 145 and 176
The greatest common divisor (GCD) of 145 and 176 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 145 and 176?
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 | 145 ÷ 176 = 0 remainder 145 |
| 2 | 176 ÷ 145 = 1 remainder 31 |
| 3 | 145 ÷ 31 = 4 remainder 21 |
| 4 | 31 ÷ 21 = 1 remainder 10 |
| 5 | 21 ÷ 10 = 2 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 156 and 197 | 1 |
| 178 and 100 | 2 |
| 99 and 171 | 9 |
| 33 and 160 | 1 |
| 90 and 87 | 3 |