How to Find GCF of 905/71, 743/27, 310/14?

GCF of 905/71, 743/27, 310/14

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 905/71, 743/27, 310/14 i.e 1/26838 easily. The following is the detailed procedure to determine the greatest common factor of fractions 905/71, 743/27, 310/14.

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 905/71,743/27,310/14?

Given fractions are 905/71,743/27,310/14

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 905/71,743/27,310/14, numerators are 905,743,310

Denominators are 71,27,14

The GCF of 905,743,310 is 1 .

LCM of 71,27,14 is 26838.

The greatest common factor of 905/71,743/27,310/14 = [GCF of 905,743,310]/[LCM of 71,27,14]= 1/26838

Therefore, the GCF of 905/71,743/27,310/14 is 1/26838.

Greatest Common Factor of 905,743,310

To find the highest common factor of 905,743,310, we have to find the factors of both numbers and list the highest common factor.

The factors of 905 are 1, 5, 181, 905

The factors of 743 are 1, 743

The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310

The HCF of 905,743,310 is 1.

Lets's calculate GCF of 905,743,310

Greatest Common Factor (GCF) of 905,743,310 By Common Division

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

Greatest Common Factor of 905,743,310 By Matching Biggest Common Factor Method

Now, list down the factors of 905

1,5,181,905

Now, list down the factors of 743

1,743

Now, list down the factors of 310

1,2,5,10,31,62,155,310

Greatest Common Factor

We found the factors 905,743,310 . The biggest common factor number is the GCF number.
So the greatest common factor 905,743,310 is 1.

Lets's calculate LCM of 71,27,14

Lowest Common Multiple of 71,27,14 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 26838

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/26838

Therefore, the GCF of Fractions 905/71,743/27,310/14 is 1/26838

Least Common Multiple of 71,27,14 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 71,27,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(71,27,14) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(71,27,14) x common factors =1 x 1 = 1

LCM(71,27,14) = ( 71 × 27 × 14 ) / 1

LCM(71,27,14) = 26838 / 1

LCM(71,27,14) = 26838

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 905/71, 743/27, 310/14

1. What is the HCF of 905,743,310?

The HCF of 905,743,310 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 905/71, 743/27, 310/14?

Answer: GCF of Numerators as per given numbers 905/71, 743/27, 310/14 is

GCF of Numerators i.e. for 905,743,310 is 1

LCM of denominators i.e. for 71,27,14 is 26838.

Thus, GCF of Fractions is 1/26838.Finally, GCF of Fractions for 905/71, 743/27, 310/14 is 1/26838.