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# GCD calculator

Find Greatest Common Divisor (GCD) of two or more numbers using four different methods.

GCD Calculator
four calculation methods with steps for each of them
show help ↓↓ examples ↓↓
Find GCD using prime factorization method
Find GCD using repeated division method
Euclidean Algorithm (works for two numbers)
Listing out the factors
working...
examples
example 1:ex 1:
What is the Greatest Common Divisor (GCD) of 104 and 64?
example 2:ex 2:
Find GCD of 96, 144 and 192 using a repeated division.
example 3:ex 3:
Find GCD of 54 and 60 using an Euclidean Algorithm.
example 4:ex 4:
Find GCD of 72 and 54 by listing out the factors.

## GCD methods

This calculator uses four methods to find GCD. We will show them using an examples.

### Method 1 : Find GCD using prime factorization method

Example: find GCD of 36 and 48

Step 1: find prime factorization of each number:

42 = 2 * 3 * 7

70 = 2 * 5 * 7

Step 2: circle out all common factors:

42 = * 3 *

70 = * 5 *

We see that the GCD is * = 14

### Method 2 : Find GCD using a repeated division

Example: find GCD of 84 and 140.

Step 1: Place the numbers inside division bar:

 84 140

Step 2: Divide both numbers by 2:

 2 84 140 42 70

Step 3: Continue to divide until the numbers do not have a common factor.

 ② 84 140 ② 42 70 ⑦ 21 35 3 7

Step 4: The GCD of 84 and 140 is: * * = 28

### Method 3 : Euclidean algorithm

Example: Find GCD of 52 and 36, using Euclidean algorithm.

Solution: Divide 52 by 36 and get the reminder, than divide 36 with the reminder from previous step. When the reminder is zero the GCD is the last divisor.

 52 : 36 = 1 reminder (16) 36 : 16 = 1 reminder (4) 16 : ④ = 4 reminder (0)

We conclude that the GCD = 4.

### Method 4 : Listing out the factors

Example: find GCD of 45 and 54 by listing out the factors.

Step 1: Find all divisors of the given numbers:

The divisors of 45 are 1, 3, 5, , 15 and 45

The divisors of 54 are 1, 2, 3, 6, 18, 27 and 54

Step 2: The greatest divisor =

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