How to Find GCF of 27/115, 31/107, 969/211?

GCF of 27/115, 31/107, 969/211

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 27/115, 31/107, 969/211 i.e 1/2596355 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/115, 31/107, 969/211.

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 27/115,31/107,969/211?

Given fractions are 27/115,31/107,969/211

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 27/115,31/107,969/211, numerators are 27,31,969

Denominators are 115,107,211

The GCF of 27,31,969 is 1 .

LCM of 115,107,211 is 2596355.

The greatest common factor of 27/115,31/107,969/211 = [GCF of 27,31,969]/[LCM of 115,107,211]= 1/2596355

Therefore, the GCF of 27/115,31/107,969/211 is 1/2596355.

Greatest Common Factor of 27,31,969

To find the highest common factor of 27,31,969, we have to find the factors of both numbers and list the highest common factor.

The factors of 27 are 1, 3, 9, 27

The factors of 31 are 1, 31

The factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969

The HCF of 27,31,969 is 1.

Lets's calculate GCF of 27,31,969

Greatest Common Factor (GCF) of 27,31,969 By Common Division

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

Greatest Common Factor of 27,31,969 By Matching Biggest Common Factor Method

Now, list down the factors of 27

1,3,9,27

Now, list down the factors of 31

1,31

Now, list down the factors of 969

1,3,17,19,51,57,323,969

Greatest Common Factor

We found the factors 27,31,969 . The biggest common factor number is the GCF number.
So the greatest common factor 27,31,969 is 1.

Lets's calculate LCM of 115,107,211

Lowest Common Multiple of 115,107,211 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 2596355

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2596355

Therefore, the GCF of Fractions 27/115,31/107,969/211 is 1/2596355

Least Common Multiple of 115,107,211 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 115,107,211 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(115,107,211) = 1

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

GCF(115,107,211) x common factors =1 x 1 = 1

LCM(115,107,211) = ( 115 × 107 × 211 ) / 1

LCM(115,107,211) = 2596355 / 1

LCM(115,107,211) = 2596355

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FAQs on GCF of Fractions of 27/115, 31/107, 969/211

1. What is the HCF of 27,31,969?

The HCF of 27,31,969 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 27/115, 31/107, 969/211?

Answer: GCF of Numerators as per given numbers 27/115, 31/107, 969/211 is

GCF of Numerators i.e. for 27,31,969 is 1

LCM of denominators i.e. for 115,107,211 is 2596355.

Thus, GCF of Fractions is 1/2596355.Finally, GCF of Fractions for 27/115, 31/107, 969/211 is 1/2596355.