Greatest Common Factor of 314/15, 422/35, 296/60

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 314/15, 422/35, 296/60

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 314/15,422/35,296/60

Given fractions are 314/15,422/35,296/60

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 314,422,296

Greatest Common Factor of Numerators i.e. GCF of 314,422,296 is 2 .

LCM of Denominators means LCM of 15,35,60 as per the given fractions.

LCM of 15,35,60 is 420 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 314,422,296

GCF of Fractions 314/15,422/35,296/60 is 2/420

2 314, 422, 296
157, 211, 148

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

Greatest Common Factor of 314,422,296 By Matching Biggest Common Factor Method

Greatest Common Factor of 314,422,296 By Matching Biggest Common Factor Method

Factors of 314

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

1,2,157,314

Factors of 422

List of positive integer factors of 422 that divides 422 without a remainder.

1,2,211,422

Factors of 296

List of positive integer factors of 296 that divides 296 without a remainder.

1,2,4,8,37,74,148,296

Greatest Common Factor

We found the factors 314,422,296 . The biggest common factor number is the GCF number.
So the greatest common factor 314,422,296 is 2.

Lets's calculate LCM of 15,35,60

3 15, 35, 60
5 5, 35, 20
1, 7, 4

∴ So the LCM of the given numbers is 3 x 5 x 1 x 7 x 4 = 420

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/420

Therefore, the GCF of Fractions 314/15,422/35,296/60 is 2/420

Least Common Multiple of 15,35,60 with GCF Formula

Least Common Multiple of 15,35,60 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 15,35,60 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(15,35,60) = 5

common factors(in case of two or more numbers have common factors) = 15

GCF(15,35,60) x common factors =5 x 15 = 75

LCM(15,35,60) = ( 15 × 35 × 60 ) / 75

LCM(15,35,60) = 31500 / 75

LCM(15,35,60) = 420


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 314/15, 422/35, 296/60

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 314/15, 422/35, 296/60?

Answer: GCF of Numerators as per given numbers 314/15, 422/35, 296/60 is

GCF of Numerators i.e. for 314,422,296 is 2

LCM of denominators i.e. for 15,35,60 is 420.

Thus, GCF of Fractions is 2/420.Finally, GCF of Fractions for 314/15, 422/35, 296/60 is 2/420.