Greatest Common Factor of 51/70, 296/75, 680/31

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 51/70, 296/75, 680/31

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 51/70,296/75,680/31

Given fractions are 51/70,296/75,680/31

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 51,296,680

Greatest Common Factor of Numerators i.e. GCF of 51,296,680 is 1 .

LCM of Denominators means LCM of 70,75,31 as per the given fractions.

LCM of 70,75,31 is 32550 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 51,296,680

GCF of Fractions 51/70,296/75,680/31 is 1/32550

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

Greatest Common Factor of 51,296,680 By Matching Biggest Common Factor Method

Greatest Common Factor of 51,296,680 By Matching Biggest Common Factor Method

Factors of 51

List of positive integer factors of 51 that divides 51 without a remainder.

1,3,17,51

Factors of 296

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

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

Factors of 680

List of positive integer factors of 680 that divides 680 without a remainder.

1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680

Greatest Common Factor

We found the factors 51,296,680 . The biggest common factor number is the GCF number.
So the greatest common factor 51,296,680 is 1.

Lets's calculate LCM of 70,75,31

5 70, 75, 31
14, 15, 31

∴ So the LCM of the given numbers is 5 x 14 x 15 x 31 = 32550

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/32550

Therefore, the GCF of Fractions 51/70,296/75,680/31 is 1/32550

Least Common Multiple of 70,75,31 with GCF Formula

Least Common Multiple of 70,75,31 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 70,75,31 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(70,75,31) = 1

common factors(in case of two or more numbers have common factors) = 5

GCF(70,75,31) x common factors =1 x 5 = 5

LCM(70,75,31) = ( 70 × 75 × 31 ) / 5

LCM(70,75,31) = 162750 / 5

LCM(70,75,31) = 32550


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 51/70, 296/75, 680/31

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 51/70, 296/75, 680/31?

Answer: GCF of Numerators as per given numbers 51/70, 296/75, 680/31 is

GCF of Numerators i.e. for 51,296,680 is 1

LCM of denominators i.e. for 70,75,31 is 32550.

Thus, GCF of Fractions is 1/32550.Finally, GCF of Fractions for 51/70, 296/75, 680/31 is 1/32550.