Greatest Common Factor of 45/31, 92/378, 314/459

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 45/31, 92/378, 314/459

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 45/31,92/378,314/459

Given fractions are 45/31,92/378,314/459

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 45,92,314

Greatest Common Factor of Numerators i.e. GCF of 45,92,314 is 1 .

LCM of Denominators means LCM of 31,378,459 as per the given fractions.

LCM of 31,378,459 is 199206 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 45,92,314

GCF of Fractions 45/31,92/378,314/459 is 1/199206

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 45,92,314 By Matching Biggest Common Factor Method

Greatest Common Factor of 45,92,314 By Matching Biggest Common Factor Method

Factors of 45

List of positive integer factors of 45 that divides 45 without a remainder.

1,3,5,9,15,45

Factors of 92

List of positive integer factors of 92 that divides 92 without a remainder.

1,2,4,23,46,92

Factors of 314

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

1,2,157,314

Greatest Common Factor

We found the factors 45,92,314 . The biggest common factor number is the GCF number.
So the greatest common factor 45,92,314 is 1.

Lets's calculate LCM of 31,378,459

3 31, 378, 459
3 31, 126, 153
3 31, 42, 51
31, 14, 17

∴ So the LCM of the given numbers is 3 x 3 x 3 x 31 x 14 x 17 = 199206

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/199206

Therefore, the GCF of Fractions 45/31,92/378,314/459 is 1/199206

Least Common Multiple of 31,378,459 with GCF Formula

Least Common Multiple of 31,378,459 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 31,378,459 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,378,459) = 1

common factors(in case of two or more numbers have common factors) = 27

GCF(31,378,459) x common factors =1 x 27 = 27

LCM(31,378,459) = ( 31 × 378 × 459 ) / 27

LCM(31,378,459) = 5378562 / 27

LCM(31,378,459) = 199206


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 45/31, 92/378, 314/459

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 45/31, 92/378, 314/459?

Answer: GCF of Numerators as per given numbers 45/31, 92/378, 314/459 is

GCF of Numerators i.e. for 45,92,314 is 1

LCM of denominators i.e. for 31,378,459 is 199206.

Thus, GCF of Fractions is 1/199206.Finally, GCF of Fractions for 45/31, 92/378, 314/459 is 1/199206.