Greatest Common Factor of 72/78, 78/38, 69/86, 32/34

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 72/78, 78/38, 69/86, 32/34

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 72/78,78/38,69/86,32/34

Given fractions are 72/78,78/38,69/86,32/34

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 72,78,69,32

Greatest Common Factor of Numerators i.e. GCF of 72,78,69,32 is 1 .

LCM of Denominators means LCM of 78,38,86,34 as per the given fractions.

LCM of 78,38,86,34 is 1083342 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 72,78,69,32

GCF of Fractions 72/78,78/38,69/86,32/34 is 1/1083342

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

Greatest Common Factor of 72,78,69,32 By Matching Biggest Common Factor Method

Greatest Common Factor of 72,78,69,32 By Matching Biggest Common Factor Method

Factors of 72

List of positive integer factors of 72 that divides 72 without a remainder.

1,2,3,4,6,8,9,12,18,24,36,72

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 69

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

1,3,23,69

Factors of 32

List of positive integer factors of 32 that divides 32 without a remainder.

1,2,4,8,16,32

Greatest Common Factor

We found the factors 72,78,69,32 . The biggest common factor number is the GCF number.
So the greatest common factor 72,78,69,32 is 1.

Lets's calculate LCM of 78,38,86,34

2 78, 38, 86, 34
39, 19, 43, 17

∴ So the LCM of the given numbers is 2 x 39 x 19 x 43 x 17 = 1083342

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1083342

Therefore, the GCF of Fractions 72/78,78/38,69/86,32/34 is 1/1083342

Least Common Multiple of 78,38,86,34 with GCF Formula

Least Common Multiple of 78,38,86,34 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 78,38,86,34 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,38,86,34) = 2

common factors(in case of two or more numbers have common factors) = 4

GCF(78,38,86,34) x common factors =2 x 4 = 8

LCM(78,38,86,34) = ( 78 × 38 × 86 × 34 ) / 8

LCM(78,38,86,34) = 8666736 / 8

LCM(78,38,86,34) = 1083342


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 72/78, 78/38, 69/86, 32/34

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 72/78, 78/38, 69/86, 32/34?

Answer: GCF of Numerators as per given numbers 72/78, 78/38, 69/86, 32/34 is

GCF of Numerators i.e. for 72,78,69,32 is 1

LCM of denominators i.e. for 78,38,86,34 is 1083342.

Thus, GCF of Fractions is 1/1083342.Finally, GCF of Fractions for 72/78, 78/38, 69/86, 32/34 is 1/1083342.