Greatest Common Factor of 33/8, 13/4, 14/5, 82/9, 240/9, 77/4, 19/9, 539/2, 76/8, 42/1

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 33/8, 13/4, 14/5, 82/9, 240/9, 77/4, 19/9, 539/2, 76/8, 42/1

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 33/8,13/4,14/5,82/9,240/9,77/4,19/9,539/2,76/8,42/1

Given fractions are 33/8,13/4,14/5,82/9,240/9,77/4,19/9,539/2,76/8,42/1

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 33,13,14,82,240,77,19,539,76,42

Greatest Common Factor of Numerators i.e. GCF of 33,13,14,82,240,77,19,539,76,42 is 1 .

LCM of Denominators means LCM of 8,4,5,9,9,4,9,2,8,1 as per the given fractions.

LCM of 8,4,5,9,9,4,9,2,8,1 is 360 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 33,13,14,82,240,77,19,539,76,42

GCF of Fractions 33/8,13/4,14/5,82/9,240/9,77/4,19/9,539/2,76/8,42/1 is 1/360

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

Greatest Common Factor of 33,13,14,82,240,77,19,539,76,42 By Matching Biggest Common Factor Method

Greatest Common Factor of 33,13,14,82,240,77,19,539,76,42 By Matching Biggest Common Factor Method

Factors of 33

List of positive integer factors of 33 that divides 33 without a remainder.

1,3,11,33

Factors of 13

List of positive integer factors of 13 that divides 13 without a remainder.

1,13

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1,2,7,14

Factors of 82

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

1,2,41,82

Factors of 240

List of positive integer factors of 240 that divides 240 without a remainder.

1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,48,60,80,120,240

Factors of 77

List of positive integer factors of 77 that divides 77 without a remainder.

1,7,11,77

Factors of 19

List of positive integer factors of 19 that divides 19 without a remainder.

1,19

Factors of 539

List of positive integer factors of 539 that divides 539 without a remainder.

1,7,11,49,77,539

Factors of 76

List of positive integer factors of 76 that divides 76 without a remainder.

1,2,4,19,38,76

Factors of 42

List of positive integer factors of 42 that divides 42 without a remainder.

1,2,3,6,7,14,21,42

Greatest Common Factor

We found the factors 33,13,14,82,240,77,19,539,76,42 . The biggest common factor number is the GCF number.
So the greatest common factor 33,13,14,82,240,77,19,539,76,42 is 1.

Lets's calculate LCM of 8,4,5,9,9,4,9,2,8,1

2 8, 4, 5, 9, 9, 4, 9, 2, 8, 1
2 4, 2, 5, 9, 9, 2, 9, 1, 4, 1
2 1, 1, 5, 9, 9, 2, 9, 1, 2, 1
3 1, 1, 5, 9, 9, 1, 9, 1, 1, 1
3 1, 1, 5, 3, 3, 1, 3, 1, 1, 1
1, 1, 5, 1, 1, 1, 1, 1, 1, 1

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 3 x 1 x 1 x 5 x 1 x 1 x 1 x 1 x 1 x 1 x 1 = 360

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/360

Therefore, the GCF of Fractions 33/8,13/4,14/5,82/9,240/9,77/4,19/9,539/2,76/8,42/1 is 1/360

Least Common Multiple of 8,4,5,9,9,4,9,2,8,1 with GCF Formula

Least Common Multiple of 8,4,5,9,9,4,9,2,8,1 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 8,4,5,9,9,4,9,2,8,1 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(8,4,5,9,9,4,9,2,8,1) = 1

common factors(in case of two or more numbers have common factors) = 20736

GCF(8,4,5,9,9,4,9,2,8,1) x common factors =1 x 20736 = 20736

LCM(8,4,5,9,9,4,9,2,8,1) = ( 8 × 4 × 5 × 9 × 9 × 4 × 9 × 2 × 8 × 1 ) / 20736

LCM(8,4,5,9,9,4,9,2,8,1) = 7464960 / 20736

LCM(8,4,5,9,9,4,9,2,8,1) = 360


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 33/8, 13/4, 14/5, 82/9, 240/9, 77/4, 19/9, 539/2, 76/8, 42/1

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 33/8, 13/4, 14/5, 82/9, 240/9, 77/4, 19/9, 539/2, 76/8, 42/1?

Answer: GCF of Numerators as per given numbers 33/8, 13/4, 14/5, 82/9, 240/9, 77/4, 19/9, 539/2, 76/8, 42/1 is

GCF of Numerators i.e. for 33,13,14,82,240,77,19,539,76,42 is 1

LCM of denominators i.e. for 8,4,5,9,9,4,9,2,8,1 is 360.

Thus, GCF of Fractions is 1/360.Finally, GCF of Fractions for 33/8, 13/4, 14/5, 82/9, 240/9, 77/4, 19/9, 539/2, 76/8, 42/1 is 1/360.