GCD of 378, 614, 678, 114 Calculator

Given Input numbers are 378, 614, 678, 114

To find the GCD of numbers using factoring list out all the divisors of each number

Divisors of 378

List of positive integer divisors of 378 that divides 378 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378

Divisors of 614

List of positive integer divisors of 614 that divides 614 without a remainder.

1, 2, 307, 614

Divisors of 678

List of positive integer divisors of 678 that divides 678 without a remainder.

1, 2, 3, 6, 113, 226, 339, 678

Divisors of 114

List of positive integer divisors of 114 that divides 114 without a remainder.

1, 2, 3, 6, 19, 38, 57, 114

Greatest Common Divisior

We found the divisors of 378, 614, 678, 114 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 378, 614, 678, 114 is 2.

Therefore, GCD of numbers 378, 614, 678, 114 is 2

Given Input Data is 378, 614, 678, 114

Make a list of Prime Factors of all the given numbers initially

Prime Factorization of 378 is 2 x 3 x 3 x 3 x 7

Prime Factorization of 614 is 2 x 307

Prime Factorization of 678 is 2 x 3 x 113

Prime Factorization of 114 is 2 x 3 x 19

Highest common occurrences in the given inputs are 2¹

Multiplying them we get the GCD as 2

Step1:

Let's calculate the GCD of first two numbers

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

LCM(378, 614) = 116046

GCD(378, 614) = ( 378 x 614 ) / 116046

GCD(378, 614) = 232092 / 116046

GCD(378, 614) = 2

Step2:

Here we consider the GCD from the above i.e. 2 as first number and the next as 678

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

LCM(2, 678) = 678

GCD(2, 678) = ( 2 x 678 ) / 678

GCD(2, 678) = 1356 / 678

GCD(2, 678) = 2

Step3:

Here we consider the GCD from the above i.e. 2 as first number and the next as 114

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

LCM(2, 114) = 114

GCD(2, 114) = ( 2 x 114 ) / 114

GCD(2, 114) = 228 / 114

GCD(2, 114) = 2

GCD of 378, 614, 678, 114 is 2

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1. What is the GCD of 378, 614, 678, 114?

GCD of 378, 614, 678, 114 is 2

2. Where do I get the detailed procedure to find GCD of 378, 614, 678, 114?

You can find a detailed procedure to find GCD of 378, 614, 678, 114 on our page.

3. How to find GCD of 378, 614, 678, 114 on a calculator?

You can find the GCD of 378, 614, 678, 114 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.