GCD of 344, 314, 678, 750 Calculator

Given Input numbers are 344, 314, 678, 750

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

Divisors of 344

List of positive integer divisors of 344 that divides 344 without a remainder.

1, 2, 4, 8, 43, 86, 172, 344

Divisors of 314

List of positive integer divisors of 314 that divides 314 without a remainder.

1, 2, 157, 314

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 750

List of positive integer divisors of 750 that divides 750 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750

Greatest Common Divisior

We found the divisors of 344, 314, 678, 750 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 344, 314, 678, 750 is 2.

Therefore, GCD of numbers 344, 314, 678, 750 is 2

Given Input Data is 344, 314, 678, 750

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

Prime Factorization of 344 is 2 x 2 x 2 x 43

Prime Factorization of 314 is 2 x 157

Prime Factorization of 678 is 2 x 3 x 113

Prime Factorization of 750 is 2 x 3 x 5 x 5 x 5

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(344, 314) = 54008

GCD(344, 314) = ( 344 x 314 ) / 54008

GCD(344, 314) = 108016 / 54008

GCD(344, 314) = 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 750

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

LCM(2, 750) = 750

GCD(2, 750) = ( 2 x 750 ) / 750

GCD(2, 750) = 1500 / 750

GCD(2, 750) = 2

GCD of 344, 314, 678, 750 is 2

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1. What is the GCD of 344, 314, 678, 750?

GCD of 344, 314, 678, 750 is 2

2. Where do I get the detailed procedure to find GCD of 344, 314, 678, 750?

You can find a detailed procedure to find GCD of 344, 314, 678, 750 on our page.

3. How to find GCD of 344, 314, 678, 750 on a calculator?

You can find the GCD of 344, 314, 678, 750 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.