GCD of 684, 312, 216, 417 Calculator

Given Input numbers are 684, 312, 216, 417

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

Divisors of 684 :

The positive integer divisors of 684 that completely divides 684 are.

1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684

Divisors of 312 :

The positive integer divisors of 312 that completely divides 312 are.

1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312

Divisors of 216 :

The positive integer divisors of 216 that completely divides 216 are.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

Divisors of 417 :

The positive integer divisors of 417 that completely divides 417 are.

1, 3, 139, 417

GCD of numbers is the greatest common divisor

So, the GCD (684, 312, 216, 417) = 3.

Given numbers are 684, 312, 216, 417

The list of prime factors of all numbers are

Prime factors of 684 are 2 x 2 x 3 x 3 x 19

Prime factors of 312 are 2 x 2 x 2 x 3 x 13

Prime factors of 216 are 2 x 2 x 2 x 3 x 3 x 3

Prime factors of 417 are 3 x 139

The highest common occurrence is 3¹

Therefore, GCD of 684, 312, 216, 417 is 3.

Given numbers are 684, 312, 216, 417

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

Apply this formula for all numbers.

Step1:

LCM(684, 312) = 17784

GCD(684, 312) = ( 684 x 312 ) / 17784

= 684 / 312

= 684

Step2:

LCM(12, 216) = 216

GCD(12, 216) = ( 12 x 216 ) / 216

= 12 / 216

= 12

Step3:

LCM(12, 417) = 1668

GCD(12, 417) = ( 12 x 417 ) / 1668

= 12 / 417

= 12

So, Greatest Common Divisor of 684, 312, 216, 417 is 3

Here are some samples of GCD of Numbers calculations.

• GCD of 716, 560, 269, 242
• GCD of 211, 704, 317, 434
• GCD of 655, 503, 445, 498
• GCD of 507, 675, 708, 458
• GCD of 438, 137, 674, 211

Given numbers are 684, 312, 216, 417
The greatest common divisor of numbers 684, 312, 216, 417 can be found in various methods such as the LCM formula, factoring, and prime factorization. The GCD of numbers 684, 312, 216, 417 is 3.

1. What is the GCD of 684, 312, 216, 417?

GCD of given numbers 684, 312, 216, 417 is 3

2. How to calculate the greatest common divisor of 684, 312, 216, 417?

We can find the highest common divisor of 684, 312, 216, 417 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 684, 312, 216, 417 i.e 3.

3. How can I use the GCD of 684, 312, 216, 417Calculator?

Out the numbers 684, 312, 216, 417 into the GCD calculator and hit the calculate button to get the greatest common divisor as result.