Greatest Common Factor of 69/34, 67/78, 31/58, 12/667

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 69/34, 67/78, 31/58, 12/667

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 69/34,67/78,31/58,12/667

Given fractions are 69/34,67/78,31/58,12/667

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 69,67,31,12

Greatest Common Factor of Numerators i.e. GCF of 69,67,31,12 is 1 .

LCM of Denominators means LCM of 34,78,58,667 as per the given fractions.

LCM of 34,78,58,667 is 884442 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 69,67,31,12

GCF of Fractions 69/34,67/78,31/58,12/667 is 1/884442

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

Greatest Common Factor of 69,67,31,12 By Matching Biggest Common Factor Method

Greatest Common Factor of 69,67,31,12 By Matching Biggest Common Factor Method

Factors of 69

List of positive integer factors of 69 that divides 69 without a remainder.

1,3,23,69

Factors of 67

List of positive integer factors of 67 that divides 67 without a remainder.

1,67

Factors of 31

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

1,31

Factors of 12

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

1,2,3,4,6,12

Greatest Common Factor

We found the factors 69,67,31,12 . The biggest common factor number is the GCF number.
So the greatest common factor 69,67,31,12 is 1.

Lets's calculate LCM of 34,78,58,667

2 34, 78, 58, 667
29 17, 39, 29, 667
17, 39, 1, 23

∴ So the LCM of the given numbers is 2 x 29 x 17 x 39 x 1 x 23 = 884442

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/884442

Therefore, the GCF of Fractions 69/34,67/78,31/58,12/667 is 1/884442

Least Common Multiple of 34,78,58,667 with GCF Formula

Least Common Multiple of 34,78,58,667 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 34,78,58,667 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(34,78,58,667) = 1

common factors(in case of two or more numbers have common factors) = 116

GCF(34,78,58,667) x common factors =1 x 116 = 116

LCM(34,78,58,667) = ( 34 × 78 × 58 × 667 ) / 116

LCM(34,78,58,667) = 102595272 / 116

LCM(34,78,58,667) = 884442


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 69/34, 67/78, 31/58, 12/667

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 69/34, 67/78, 31/58, 12/667?

Answer: GCF of Numerators as per given numbers 69/34, 67/78, 31/58, 12/667 is

GCF of Numerators i.e. for 69,67,31,12 is 1

LCM of denominators i.e. for 34,78,58,667 is 884442.

Thus, GCF of Fractions is 1/884442.Finally, GCF of Fractions for 69/34, 67/78, 31/58, 12/667 is 1/884442.