How to Find GCF of 191/71, 160/98, 103/78?

GCF of 191/71, 160/98, 103/78

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 191/71, 160/98, 103/78 i.e 1/271362 easily. The following is the detailed procedure to determine the greatest common factor of fractions 191/71, 160/98, 103/78.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 191/71,160/98,103/78?

Given fractions are 191/71,160/98,103/78

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 191/71,160/98,103/78, numerators are 191,160,103

Denominators are 71,98,78

The GCF of 191,160,103 is 1 .

LCM of 71,98,78 is 271362.

The greatest common factor of 191/71,160/98,103/78 = [GCF of 191,160,103]/[LCM of 71,98,78]= 1/271362

Therefore, the GCF of 191/71,160/98,103/78 is 1/271362.

Greatest Common Factor of 191,160,103

To find the highest common factor of 191,160,103, we have to find the factors of both numbers and list the highest common factor.

The factors of 191 are 1, 191

The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160

The factors of 103 are 1, 103

The HCF of 191,160,103 is 1.

Lets's calculate GCF of 191,160,103

Greatest Common Factor (GCF) of 191,160,103 By Common Division

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

Greatest Common Factor of 191,160,103 By Matching Biggest Common Factor Method

Now, list down the factors of 191

1,191

Now, list down the factors of 160

1,2,4,5,8,10,16,20,32,40,80,160

Now, list down the factors of 103

1,103

Greatest Common Factor

We found the factors 191,160,103 . The biggest common factor number is the GCF number.
So the greatest common factor 191,160,103 is 1.

Lets's calculate LCM of 71,98,78

Lowest Common Multiple of 71,98,78 using Common Division

2	71, 98, 78
	71, 49, 39

∴ So the LCM of the given numbers is 2 x 71 x 49 x 39 = 271362

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/271362

Therefore, the GCF of Fractions 191/71,160/98,103/78 is 1/271362

Least Common Multiple of 71,98,78 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 71,98,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(71,98,78) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(71,98,78) x common factors =1 x 2 = 2

LCM(71,98,78) = ( 71 × 98 × 78 ) / 2

LCM(71,98,78) = 542724 / 2

LCM(71,98,78) = 271362

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FAQs on GCF of Fractions of 191/71, 160/98, 103/78

1. What is the HCF of 191,160,103?

The HCF of 191,160,103 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. 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.

4. What is the GCF of Fractions for 191/71, 160/98, 103/78?

Answer: GCF of Numerators as per given numbers 191/71, 160/98, 103/78 is

GCF of Numerators i.e. for 191,160,103 is 1

LCM of denominators i.e. for 71,98,78 is 271362.

Thus, GCF of Fractions is 1/271362.Finally, GCF of Fractions for 191/71, 160/98, 103/78 is 1/271362.