Greatest Common Divisor (GCD) of 21 and 16
The greatest common divisor (GCD) of 21 and 16 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 21 and 16?
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 | 21 ÷ 16 = 1 remainder 5 |
| 2 | 16 ÷ 5 = 3 remainder 1 |
| 3 | 5 ÷ 1 = 5 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 158 and 29 | 1 |
| 39 and 46 | 1 |
| 173 and 127 | 1 |
| 141 and 45 | 3 |
| 36 and 86 | 2 |