Greatest Common Factor of 40/56, 34/37, 312/814

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 40/56, 34/37, 312/814

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

Greatest Common Factor of 40/56,34/37,312/814

Given fractions are 40/56,34/37,312/814

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 40,34,312

Greatest Common Factor of Numerators i.e. GCF of 40,34,312 is 2 .

LCM of Denominators means LCM of 56,37,814 as per the given fractions.

LCM of 56,37,814 is 22792 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 40,34,312

GCF of Fractions 40/56,34/37,312/814 is 2/22792

2 40, 34, 312
20, 17, 156

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 40,34,312 By Matching Biggest Common Factor Method

Greatest Common Factor of 40,34,312 By Matching Biggest Common Factor Method

Factors of 40

List of positive integer factors of 40 that divides 40 without a remainder.

1,2,4,5,8,10,20,40

Factors of 34

List of positive integer factors of 34 that divides 34 without a remainder.

1,2,17,34

Factors of 312

List of positive integer factors of 312 that divides 312 without a remainder.

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

Greatest Common Factor

We found the factors 40,34,312 . The biggest common factor number is the GCF number.
So the greatest common factor 40,34,312 is 2.

Lets's calculate LCM of 56,37,814

2 56, 37, 814
37 28, 37, 407
28, 1, 11

∴ So the LCM of the given numbers is 2 x 37 x 28 x 1 x 11 = 22792

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/22792

Therefore, the GCF of Fractions 40/56,34/37,312/814 is 2/22792

Least Common Multiple of 56,37,814 with GCF Formula

Least Common Multiple of 56,37,814 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 56,37,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(56,37,814) = 1

common factors(in case of two or more numbers have common factors) = 74

GCF(56,37,814) x common factors =1 x 74 = 74

LCM(56,37,814) = ( 56 × 37 × 814 ) / 74

LCM(56,37,814) = 1686608 / 74

LCM(56,37,814) = 22792


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 40/56, 34/37, 312/814

1. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

2. What is the GCF of Fractions for 40/56, 34/37, 312/814?

Answer: GCF of Numerators as per given numbers 40/56, 34/37, 312/814 is

GCF of Numerators i.e. for 40,34,312 is 2

LCM of denominators i.e. for 56,37,814 is 22792.

Thus, GCF of Fractions is 2/22792.Finally, GCF of Fractions for 40/56, 34/37, 312/814 is 2/22792.