Greatest Common Factor of 46/2, 80/5, 52/4, 91/9, 413/1, 80/2, 38/2, 693/9, 49/1, 31/4

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 46/2, 80/5, 52/4, 91/9, 413/1, 80/2, 38/2, 693/9, 49/1, 31/4

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 46/2,80/5,52/4,91/9,413/1,80/2,38/2,693/9,49/1,31/4

Given fractions are 46/2,80/5,52/4,91/9,413/1,80/2,38/2,693/9,49/1,31/4

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 46,80,52,91,413,80,38,693,49,31

Greatest Common Factor of Numerators i.e. GCF of 46,80,52,91,413,80,38,693,49,31 is 1 .

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

LCM of 2,5,4,9,1,2,2,9,1,4 is 180 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 46,80,52,91,413,80,38,693,49,31

GCF of Fractions 46/2,80/5,52/4,91/9,413/1,80/2,38/2,693/9,49/1,31/4 is 1/180

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

Greatest Common Factor of 46,80,52,91,413,80,38,693,49,31 By Matching Biggest Common Factor Method

Greatest Common Factor of 46,80,52,91,413,80,38,693,49,31 By Matching Biggest Common Factor Method

Factors of 46

List of positive integer factors of 46 that divides 46 without a remainder.

1,2,23,46

Factors of 80

List of positive integer factors of 80 that divides 80 without a remainder.

1,2,4,5,8,10,16,20,40,80

Factors of 52

List of positive integer factors of 52 that divides 52 without a remainder.

1,2,4,13,26,52

Factors of 91

List of positive integer factors of 91 that divides 91 without a remainder.

1,7,13,91

Factors of 413

List of positive integer factors of 413 that divides 413 without a remainder.

1,7,59,413

Factors of 80

List of positive integer factors of 80 that divides 80 without a remainder.

1,2,4,5,8,10,16,20,40,80

Factors of 38

List of positive integer factors of 38 that divides 38 without a remainder.

1,2,19,38

Factors of 693

List of positive integer factors of 693 that divides 693 without a remainder.

1,3,7,9,11,21,33,63,77,99,231,693

Factors of 49

List of positive integer factors of 49 that divides 49 without a remainder.

1,7,49

Factors of 31

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

1,31

Greatest Common Factor

We found the factors 46,80,52,91,413,80,38,693,49,31 . The biggest common factor number is the GCF number.
So the greatest common factor 46,80,52,91,413,80,38,693,49,31 is 1.

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

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

∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 1 x 5 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 = 180

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/180

Therefore, the GCF of Fractions 46/2,80/5,52/4,91/9,413/1,80/2,38/2,693/9,49/1,31/4 is 1/180

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

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

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

common factors(in case of two or more numbers have common factors) = 288

GCF(2,5,4,9,1,2,2,9,1,4) x common factors =1 x 288 = 288

LCM(2,5,4,9,1,2,2,9,1,4) = ( 2 × 5 × 4 × 9 × 1 × 2 × 2 × 9 × 1 × 4 ) / 288

LCM(2,5,4,9,1,2,2,9,1,4) = 51840 / 288

LCM(2,5,4,9,1,2,2,9,1,4) = 180


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 46/2, 80/5, 52/4, 91/9, 413/1, 80/2, 38/2, 693/9, 49/1, 31/4

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 46/2, 80/5, 52/4, 91/9, 413/1, 80/2, 38/2, 693/9, 49/1, 31/4?

Answer: GCF of Numerators as per given numbers 46/2, 80/5, 52/4, 91/9, 413/1, 80/2, 38/2, 693/9, 49/1, 31/4 is

GCF of Numerators i.e. for 46,80,52,91,413,80,38,693,49,31 is 1

LCM of denominators i.e. for 2,5,4,9,1,2,2,9,1,4 is 180.

Thus, GCF of Fractions is 1/180.Finally, GCF of Fractions for 46/2, 80/5, 52/4, 91/9, 413/1, 80/2, 38/2, 693/9, 49/1, 31/4 is 1/180.