Greatest Common Factor of 35/48, 31/75, 19/39, 16/546

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 35/48, 31/75, 19/39, 16/546

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 35/48,31/75,19/39,16/546

Given fractions are 35/48,31/75,19/39,16/546

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 35,31,19,16

Greatest Common Factor of Numerators i.e. GCF of 35,31,19,16 is 1 .

LCM of Denominators means LCM of 48,75,39,546 as per the given fractions.

LCM of 48,75,39,546 is 109200 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 35,31,19,16

GCF of Fractions 35/48,31/75,19/39,16/546 is 1/109200

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

Greatest Common Factor of 35,31,19,16 By Matching Biggest Common Factor Method

Greatest Common Factor of 35,31,19,16 By Matching Biggest Common Factor Method

Factors of 35

List of positive integer factors of 35 that divides 35 without a remainder.

1,5,7,35

Factors of 31

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

1,31

Factors of 19

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

1,19

Factors of 16

List of positive integer factors of 16 that divides 16 without a remainder.

1,2,4,8,16

Greatest Common Factor

We found the factors 35,31,19,16 . The biggest common factor number is the GCF number.
So the greatest common factor 35,31,19,16 is 1.

Lets's calculate LCM of 48,75,39,546

2 48, 75, 39, 546
3 24, 75, 39, 273
13 8, 25, 13, 91
8, 25, 1, 7

∴ So the LCM of the given numbers is 2 x 3 x 13 x 8 x 25 x 1 x 7 = 109200

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/109200

Therefore, the GCF of Fractions 35/48,31/75,19/39,16/546 is 1/109200

Least Common Multiple of 48,75,39,546 with GCF Formula

Least Common Multiple of 48,75,39,546 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 48,75,39,546 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(48,75,39,546) = 3

common factors(in case of two or more numbers have common factors) = 234

GCF(48,75,39,546) x common factors =3 x 234 = 702

LCM(48,75,39,546) = ( 48 × 75 × 39 × 546 ) / 702

LCM(48,75,39,546) = 76658400 / 702

LCM(48,75,39,546) = 109200


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 35/48, 31/75, 19/39, 16/546

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 35/48, 31/75, 19/39, 16/546?

Answer: GCF of Numerators as per given numbers 35/48, 31/75, 19/39, 16/546 is

GCF of Numerators i.e. for 35,31,19,16 is 1

LCM of denominators i.e. for 48,75,39,546 is 109200.

Thus, GCF of Fractions is 1/109200.Finally, GCF of Fractions for 35/48, 31/75, 19/39, 16/546 is 1/109200.