# Greatest Common Divisor

The **greatest common divisor** (or** GCD**) of two or more numbers is the largest number that exactly divides all.

## Calculation of the Greatest Common Divisor

1. Decompose the numbers into prime factors.

2. Select the common factors with the smallest exponent.

#### Examples

Determine the GCD of: 72, 108 and 60:

1.

72 = 2^{3 } · 3^{2}

108 = 2^{2 } · 3^{3}

60 = 2^{2 } · 3 · 5

2.

GCD (72, 108, 60) = 2^{2 } · 3 = 12

12 is the largest number that divides 72, 108 and 60.

If a number is a divisor of another, then this number is the** GCD**.

The number 12 is a divisor of 36.

GCD (12, 36) = 12

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