GCD of 106, 214, 180 Calculator

Given Input numbers are 106, 214, 180

In the factoring method, we have to find the divisors of all numbers

Divisors of 106 :

The positive integer divisors of 106 that completely divides 106 are.

1, 2, 53, 106

Divisors of 214 :

The positive integer divisors of 214 that completely divides 214 are.

1, 2, 107, 214

Divisors of 180 :

The positive integer divisors of 180 that completely divides 180 are.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

GCD of numbers is the greatest common divisor

So, the GCD (106, 214, 180) = 2.

Given numbers are 106, 214, 180

The list of prime factors of all numbers are

Prime factors of 106 are 2 x 53

Prime factors of 214 are 2 x 107

Prime factors of 180 are 2 x 2 x 3 x 3 x 5

The highest common occurrence is 2¹

Therefore, GCD of 106, 214, 180 is 2.

Given numbers are 106, 214, 180

GCD of 2 numbers formula is GCD(a, b) = ( a x b) / LCM(a, b)

Apply this formula for all numbers.

Step1:

LCM(106, 214) = 11342

GCD(106, 214) = ( 106 x 214 ) / 11342

= 106 / 214

= 106

Step2:

LCM(2, 180) = 180

GCD(2, 180) = ( 2 x 180 ) / 180

= 2 / 180

= 2

So, Greatest Common Divisor of 106, 214, 180 is 2

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Given numbers are 106, 214, 180
The greatest common divisor of numbers 106, 214, 180 can be found in various methods such as the LCM formula, factoring, and prime factorization. The GCD of numbers 106, 214, 180 is 2.

1. What is the GCD of 106, 214, 180?

GCD of given numbers 106, 214, 180 is 2

2. How to calculate the greatest common divisor of 106, 214, 180?

We can find the highest common divisor of 106, 214, 180 easily using the prime factorization method. Just list the prime factors of all numbers and pick the highest common factor which is the GCD of 106, 214, 180 i.e 2.

3. How can I use the GCD of 106, 214, 180Calculator?

Out the numbers 106, 214, 180 into the GCD calculator and hit the calculate button to get the greatest common divisor as result.