Greatest Common Factor of 12/69, 84/28, 31/39

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 12/69, 84/28, 31/39

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 12/69,84/28,31/39

Given fractions are 12/69,84/28,31/39

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 12,84,31

Greatest Common Factor of Numerators i.e. GCF of 12,84,31 is 1 .

LCM of Denominators means LCM of 69,28,39 as per the given fractions.

LCM of 69,28,39 is 25116 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 12,84,31

GCF of Fractions 12/69,84/28,31/39 is 1/25116

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

Greatest Common Factor of 12,84,31 By Matching Biggest Common Factor Method

Greatest Common Factor of 12,84,31 By Matching Biggest Common Factor Method

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1,2,3,4,6,12

Factors of 84

List of positive integer factors of 84 that divides 84 without a remainder.

1,2,3,4,6,7,12,14,21,28,42,84

Factors of 31

List of positive integer factors of 31 that divides 31 without a remainder.

1,31

Greatest Common Factor

We found the factors 12,84,31 . The biggest common factor number is the GCF number.
So the greatest common factor 12,84,31 is 1.

Lets's calculate LCM of 69,28,39

3 69, 28, 39
23, 28, 13

∴ So the LCM of the given numbers is 3 x 23 x 28 x 13 = 25116

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/25116

Therefore, the GCF of Fractions 12/69,84/28,31/39 is 1/25116

Least Common Multiple of 69,28,39 with GCF Formula

Least Common Multiple of 69,28,39 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 69,28,39 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(69,28,39) = 1

common factors(in case of two or more numbers have common factors) = 3

GCF(69,28,39) x common factors =1 x 3 = 3

LCM(69,28,39) = ( 69 × 28 × 39 ) / 3

LCM(69,28,39) = 75348 / 3

LCM(69,28,39) = 25116


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 12/69, 84/28, 31/39

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 12/69, 84/28, 31/39?

Answer: GCF of Numerators as per given numbers 12/69, 84/28, 31/39 is

GCF of Numerators i.e. for 12,84,31 is 1

LCM of denominators i.e. for 69,28,39 is 25116.

Thus, GCF of Fractions is 1/25116.Finally, GCF of Fractions for 12/69, 84/28, 31/39 is 1/25116.