GCD of 106, 370, 678, 748 Calculator

Given Input numbers are 106, 370, 678, 748

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

Divisors of 106

List of positive integer divisors of 106 that divides 106 without a remainder.

1, 2, 53, 106

Divisors of 370

List of positive integer divisors of 370 that divides 370 without a remainder.

1, 2, 5, 10, 37, 74, 185, 370

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 748

List of positive integer divisors of 748 that divides 748 without a remainder.

1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748

Greatest Common Divisior

We found the divisors of 106, 370, 678, 748 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 106, 370, 678, 748 is 2.

Therefore, GCD of numbers 106, 370, 678, 748 is 2

Given Input Data is 106, 370, 678, 748

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

Prime Factorization of 106 is 2 x 53

Prime Factorization of 370 is 2 x 5 x 37

Prime Factorization of 678 is 2 x 3 x 113

Prime Factorization of 748 is 2 x 2 x 11 x 17

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(106, 370) = 19610

GCD(106, 370) = ( 106 x 370 ) / 19610

GCD(106, 370) = 39220 / 19610

GCD(106, 370) = 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 748

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

LCM(2, 748) = 748

GCD(2, 748) = ( 2 x 748 ) / 748

GCD(2, 748) = 1496 / 748

GCD(2, 748) = 2

GCD of 106, 370, 678, 748 is 2

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1. What is the GCD of 106, 370, 678, 748?

GCD of 106, 370, 678, 748 is 2

2. Where do I get the detailed procedure to find GCD of 106, 370, 678, 748?

You can find a detailed procedure to find GCD of 106, 370, 678, 748 on our page.

3. How to find GCD of 106, 370, 678, 748 on a calculator?

You can find the GCD of 106, 370, 678, 748 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.