How to Find GCF of 76/274, 37/647, 165/317?

GCF of 76/274, 37/647, 165/317

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 76/274, 37/647, 165/317 i.e 1/56197126 easily. The following is the detailed procedure to determine the greatest common factor of fractions 76/274, 37/647, 165/317.

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 76/274,37/647,165/317?

Given fractions are 76/274,37/647,165/317

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 76/274,37/647,165/317, numerators are 76,37,165

Denominators are 274,647,317

The GCF of 76,37,165 is 1 .

LCM of 274,647,317 is 56197126.

The greatest common factor of 76/274,37/647,165/317 = [GCF of 76,37,165]/[LCM of 274,647,317]= 1/56197126

Therefore, the GCF of 76/274,37/647,165/317 is 1/56197126.

Greatest Common Factor of 76,37,165

To find the highest common factor of 76,37,165, we have to find the factors of both numbers and list the highest common factor.

The factors of 76 are 1, 2, 4, 19, 38, 76

The factors of 37 are 1, 37

The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165

The HCF of 76,37,165 is 1.

Lets's calculate GCF of 76,37,165

Greatest Common Factor (GCF) of 76,37,165 By Common Division

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

Greatest Common Factor of 76,37,165 By Matching Biggest Common Factor Method

Now, list down the factors of 76

1,2,4,19,38,76

Now, list down the factors of 37

1,37

Now, list down the factors of 165

1,3,5,11,15,33,55,165

Greatest Common Factor

We found the factors 76,37,165 . The biggest common factor number is the GCF number.
So the greatest common factor 76,37,165 is 1.

Lets's calculate LCM of 274,647,317

Lowest Common Multiple of 274,647,317 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 56197126

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/56197126

Therefore, the GCF of Fractions 76/274,37/647,165/317 is 1/56197126

Least Common Multiple of 274,647,317 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 274,647,317 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(274,647,317) = 1

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

GCF(274,647,317) x common factors =1 x 1 = 1

LCM(274,647,317) = ( 274 × 647 × 317 ) / 1

LCM(274,647,317) = 56197126 / 1

LCM(274,647,317) = 56197126

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FAQs on GCF of Fractions of 76/274, 37/647, 165/317

1. What is the HCF of 76,37,165?

The HCF of 76,37,165 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 76/274, 37/647, 165/317?

Answer: GCF of Numerators as per given numbers 76/274, 37/647, 165/317 is

GCF of Numerators i.e. for 76,37,165 is 1

LCM of denominators i.e. for 274,647,317 is 56197126.

Thus, GCF of Fractions is 1/56197126.Finally, GCF of Fractions for 76/274, 37/647, 165/317 is 1/56197126.