Greatest Common Factor of 40/9, 12/4, 30/5, 47/8, 543/2, 77/1, 41/9, 681/2, 78/7, 27/4

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 40/9, 12/4, 30/5, 47/8, 543/2, 77/1, 41/9, 681/2, 78/7, 27/4

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 40/9,12/4,30/5,47/8,543/2,77/1,41/9,681/2,78/7,27/4

Given fractions are 40/9,12/4,30/5,47/8,543/2,77/1,41/9,681/2,78/7,27/4

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 40,12,30,47,543,77,41,681,78,27

Greatest Common Factor of Numerators i.e. GCF of 40,12,30,47,543,77,41,681,78,27 is 1 .

LCM of Denominators means LCM of 9,4,5,8,2,1,9,2,7,4 as per the given fractions.

LCM of 9,4,5,8,2,1,9,2,7,4 is 2520 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 40,12,30,47,543,77,41,681,78,27

GCF of Fractions 40/9,12/4,30/5,47/8,543/2,77/1,41/9,681/2,78/7,27/4 is 1/2520

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

Greatest Common Factor of 40,12,30,47,543,77,41,681,78,27 By Matching Biggest Common Factor Method

Greatest Common Factor of 40,12,30,47,543,77,41,681,78,27 By Matching Biggest Common Factor Method

Factors of 40

List of positive integer factors of 40 that divides 40 without a remainder.

1,2,4,5,8,10,20,40

Factors of 12

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

1,2,3,4,6,12

Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1,2,3,5,6,10,15,30

Factors of 47

List of positive integer factors of 47 that divides 47 without a remainder.

1,47

Factors of 543

List of positive integer factors of 543 that divides 543 without a remainder.

1,3,181,543

Factors of 77

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

1,7,11,77

Factors of 41

List of positive integer factors of 41 that divides 41 without a remainder.

1,41

Factors of 681

List of positive integer factors of 681 that divides 681 without a remainder.

1,3,227,681

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 27

List of positive integer factors of 27 that divides 27 without a remainder.

1,3,9,27

Greatest Common Factor

We found the factors 40,12,30,47,543,77,41,681,78,27 . The biggest common factor number is the GCF number.
So the greatest common factor 40,12,30,47,543,77,41,681,78,27 is 1.

Lets's calculate LCM of 9,4,5,8,2,1,9,2,7,4

2 9, 4, 5, 8, 2, 1, 9, 2, 7, 4
2 9, 2, 5, 4, 1, 1, 9, 1, 7, 2
3 9, 1, 5, 1, 1, 1, 9, 1, 7, 2
3 3, 1, 5, 1, 1, 1, 3, 1, 7, 2
1, 1, 5, 1, 1, 1, 1, 1, 7, 2

∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 1 x 1 x 5 x 1 x 1 x 1 x 1 x 1 x 7 x 2 = 2520

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2520

Therefore, the GCF of Fractions 40/9,12/4,30/5,47/8,543/2,77/1,41/9,681/2,78/7,27/4 is 1/2520

Least Common Multiple of 9,4,5,8,2,1,9,2,7,4 with GCF Formula

Least Common Multiple of 9,4,5,8,2,1,9,2,7,4 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 9,4,5,8,2,1,9,2,7,4 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(9,4,5,8,2,1,9,2,7,4) = 1

common factors(in case of two or more numbers have common factors) = 576

GCF(9,4,5,8,2,1,9,2,7,4) x common factors =1 x 576 = 576

LCM(9,4,5,8,2,1,9,2,7,4) = ( 9 × 4 × 5 × 8 × 2 × 1 × 9 × 2 × 7 × 4 ) / 576

LCM(9,4,5,8,2,1,9,2,7,4) = 1451520 / 576

LCM(9,4,5,8,2,1,9,2,7,4) = 2520


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 40/9, 12/4, 30/5, 47/8, 543/2, 77/1, 41/9, 681/2, 78/7, 27/4

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 40/9, 12/4, 30/5, 47/8, 543/2, 77/1, 41/9, 681/2, 78/7, 27/4?

Answer: GCF of Numerators as per given numbers 40/9, 12/4, 30/5, 47/8, 543/2, 77/1, 41/9, 681/2, 78/7, 27/4 is

GCF of Numerators i.e. for 40,12,30,47,543,77,41,681,78,27 is 1

LCM of denominators i.e. for 9,4,5,8,2,1,9,2,7,4 is 2520.

Thus, GCF of Fractions is 1/2520.Finally, GCF of Fractions for 40/9, 12/4, 30/5, 47/8, 543/2, 77/1, 41/9, 681/2, 78/7, 27/4 is 1/2520.