Greatest Common Factor of 82/69, 78/24, 74/16, 72/138

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 82/69, 78/24, 74/16, 72/138

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 82/69,78/24,74/16,72/138

Given fractions are 82/69,78/24,74/16,72/138

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 82,78,74,72

Greatest Common Factor of Numerators i.e. GCF of 82,78,74,72 is 2 .

LCM of Denominators means LCM of 69,24,16,138 as per the given fractions.

LCM of 69,24,16,138 is 1104 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 82,78,74,72

GCF of Fractions 82/69,78/24,74/16,72/138 is 2/1104

2 82, 78, 74, 72
41, 39, 37, 36

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 82,78,74,72 By Matching Biggest Common Factor Method

Greatest Common Factor of 82,78,74,72 By Matching Biggest Common Factor Method

Factors of 82

List of positive integer factors of 82 that divides 82 without a remainder.

1,2,41,82

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 74

List of positive integer factors of 74 that divides 74 without a remainder.

1,2,37,74

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

Greatest Common Factor

We found the factors 82,78,74,72 . The biggest common factor number is the GCF number.
So the greatest common factor 82,78,74,72 is 2.

Lets's calculate LCM of 69,24,16,138

2 69, 24, 16, 138
2 69, 12, 8, 69
2 69, 6, 4, 69
3 69, 3, 2, 69
23 23, 1, 2, 23
1, 1, 2, 1

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 23 x 1 x 1 x 2 x 1 = 1104

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1104

Therefore, the GCF of Fractions 82/69,78/24,74/16,72/138 is 2/1104

Least Common Multiple of 69,24,16,138 with GCF Formula

Least Common Multiple of 69,24,16,138 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 69,24,16,138 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(69,24,16,138) = 1

common factors(in case of two or more numbers have common factors) = 3312

GCF(69,24,16,138) x common factors =1 x 3312 = 3312

LCM(69,24,16,138) = ( 69 × 24 × 16 × 138 ) / 3312

LCM(69,24,16,138) = 3656448 / 3312

LCM(69,24,16,138) = 1104


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 82/69, 78/24, 74/16, 72/138

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 82/69, 78/24, 74/16, 72/138?

Answer: GCF of Numerators as per given numbers 82/69, 78/24, 74/16, 72/138 is

GCF of Numerators i.e. for 82,78,74,72 is 2

LCM of denominators i.e. for 69,24,16,138 is 1104.

Thus, GCF of Fractions is 2/1104.Finally, GCF of Fractions for 82/69, 78/24, 74/16, 72/138 is 2/1104.