Greatest Common Factor of 75/16, 45/48, 349/192

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 75/16, 45/48, 349/192

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 75/16,45/48,349/192

Given fractions are 75/16,45/48,349/192

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 75,45,349

Greatest Common Factor of Numerators i.e. GCF of 75,45,349 is 1 .

LCM of Denominators means LCM of 16,48,192 as per the given fractions.

LCM of 16,48,192 is 192 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 75,45,349

GCF of Fractions 75/16,45/48,349/192 is 1/192

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

Greatest Common Factor of 75,45,349 By Matching Biggest Common Factor Method

Greatest Common Factor of 75,45,349 By Matching Biggest Common Factor Method

Factors of 75

List of positive integer factors of 75 that divides 75 without a remainder.

1,3,5,15,25,75

Factors of 45

List of positive integer factors of 45 that divides 45 without a remainder.

1,3,5,9,15,45

Factors of 349

List of positive integer factors of 349 that divides 349 without a remainder.

1,349

Greatest Common Factor

We found the factors 75,45,349 . The biggest common factor number is the GCF number.
So the greatest common factor 75,45,349 is 1.

Lets's calculate LCM of 16,48,192

2 16, 48, 192
2 8, 24, 96
2 4, 12, 48
2 2, 6, 24
3 1, 3, 12
1, 1, 4

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 1 x 1 x 4 = 192

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/192

Therefore, the GCF of Fractions 75/16,45/48,349/192 is 1/192

Least Common Multiple of 16,48,192 with GCF Formula

Least Common Multiple of 16,48,192 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 16,48,192 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(16,48,192) = 16

common factors(in case of two or more numbers have common factors) = 48

GCF(16,48,192) x common factors =16 x 48 = 768

LCM(16,48,192) = ( 16 × 48 × 192 ) / 768

LCM(16,48,192) = 147456 / 768

LCM(16,48,192) = 192


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 75/16, 45/48, 349/192

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 75/16, 45/48, 349/192?

Answer: GCF of Numerators as per given numbers 75/16, 45/48, 349/192 is

GCF of Numerators i.e. for 75,45,349 is 1

LCM of denominators i.e. for 16,48,192 is 192.

Thus, GCF of Fractions is 1/192.Finally, GCF of Fractions for 75/16, 45/48, 349/192 is 1/192.