Greatest Common Factor of 75/28, 14/69, 29/69, 471/34

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 75/28, 14/69, 29/69, 471/34

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 75/28,14/69,29/69,471/34

Given fractions are 75/28,14/69,29/69,471/34

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 75,14,29,471

Greatest Common Factor of Numerators i.e. GCF of 75,14,29,471 is 1 .

LCM of Denominators means LCM of 28,69,69,34 as per the given fractions.

LCM of 28,69,69,34 is 32844 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 75,14,29,471

GCF of Fractions 75/28,14/69,29/69,471/34 is 1/32844

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

Greatest Common Factor of 75,14,29,471 By Matching Biggest Common Factor Method

Greatest Common Factor of 75,14,29,471 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 14

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

1,2,7,14

Factors of 29

List of positive integer factors of 29 that divides 29 without a remainder.

1,29

Factors of 471

List of positive integer factors of 471 that divides 471 without a remainder.

1,3,157,471

Greatest Common Factor

We found the factors 75,14,29,471 . The biggest common factor number is the GCF number.
So the greatest common factor 75,14,29,471 is 1.

Lets's calculate LCM of 28,69,69,34

2 28, 69, 69, 34
3 14, 69, 69, 17
23 14, 23, 23, 17
14, 1, 1, 17

∴ So the LCM of the given numbers is 2 x 3 x 23 x 14 x 1 x 1 x 17 = 32844

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/32844

Therefore, the GCF of Fractions 75/28,14/69,29/69,471/34 is 1/32844

Least Common Multiple of 28,69,69,34 with GCF Formula

Least Common Multiple of 28,69,69,34 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 28,69,69,34 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(28,69,69,34) = 1

common factors(in case of two or more numbers have common factors) = 138

GCF(28,69,69,34) x common factors =1 x 138 = 138

LCM(28,69,69,34) = ( 28 × 69 × 69 × 34 ) / 138

LCM(28,69,69,34) = 4532472 / 138

LCM(28,69,69,34) = 32844


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 75/28, 14/69, 29/69, 471/34

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 75/28, 14/69, 29/69, 471/34?

Answer: GCF of Numerators as per given numbers 75/28, 14/69, 29/69, 471/34 is

GCF of Numerators i.e. for 75,14,29,471 is 1

LCM of denominators i.e. for 28,69,69,34 is 32844.

Thus, GCF of Fractions is 1/32844.Finally, GCF of Fractions for 75/28, 14/69, 29/69, 471/34 is 1/32844.