Greatest Common Factor of 7/51, 10/72, 78/34, 34/14

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 7/51, 10/72, 78/34, 34/14

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 7/51,10/72,78/34,34/14

Given fractions are 7/51,10/72,78/34,34/14

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 7,10,78,34

Greatest Common Factor of Numerators i.e. GCF of 7,10,78,34 is 1 .

LCM of Denominators means LCM of 51,72,34,14 as per the given fractions.

LCM of 51,72,34,14 is 8568 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 7,10,78,34

GCF of Fractions 7/51,10/72,78/34,34/14 is 1/8568

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

Greatest Common Factor of 7,10,78,34 By Matching Biggest Common Factor Method

Greatest Common Factor of 7,10,78,34 By Matching Biggest Common Factor Method

Factors of 7

List of positive integer factors of 7 that divides 7 without a remainder.

1,7

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1,2,5,10

Factors of 78

List of positive integer factors of 78 that divides 78 without a remainder.

1,2,3,6,13,26,39,78

Factors of 34

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

1,2,17,34

Greatest Common Factor

We found the factors 7,10,78,34 . The biggest common factor number is the GCF number.
So the greatest common factor 7,10,78,34 is 1.

Lets's calculate LCM of 51,72,34,14

2 51, 72, 34, 14
3 51, 36, 17, 7
17 17, 12, 17, 7
1, 12, 1, 7

∴ So the LCM of the given numbers is 2 x 3 x 17 x 1 x 12 x 1 x 7 = 8568

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8568

Therefore, the GCF of Fractions 7/51,10/72,78/34,34/14 is 1/8568

Least Common Multiple of 51,72,34,14 with GCF Formula

Least Common Multiple of 51,72,34,14 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 51,72,34,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(51,72,34,14) = 1

common factors(in case of two or more numbers have common factors) = 204

GCF(51,72,34,14) x common factors =1 x 204 = 204

LCM(51,72,34,14) = ( 51 × 72 × 34 × 14 ) / 204

LCM(51,72,34,14) = 1747872 / 204

LCM(51,72,34,14) = 8568


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 7/51, 10/72, 78/34, 34/14

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 7/51, 10/72, 78/34, 34/14?

Answer: GCF of Numerators as per given numbers 7/51, 10/72, 78/34, 34/14 is

GCF of Numerators i.e. for 7,10,78,34 is 1

LCM of denominators i.e. for 51,72,34,14 is 8568.

Thus, GCF of Fractions is 1/8568.Finally, GCF of Fractions for 7/51, 10/72, 78/34, 34/14 is 1/8568.