How to Find GCF of 429/174, 6877/311?

GCF of 429/174, 6877/311

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 429/174, 6877/311 i.e 13/54114 easily. The following is the detailed procedure to determine the greatest common factor of fractions 429/174, 6877/311.

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 429/174,6877/311?

Given fractions are 429/174,6877/311

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 429/174,6877/311, numerators are 429,6877

Denominators are 174,311

The GCF of 429,6877 is 13 .

LCM of 174,311 is 54114.

The greatest common factor of 429/174,6877/311 = [GCF of 429,6877]/[LCM of 174,311]= 13/54114

Therefore, the GCF of 429/174,6877/311 is 13/54114.

Greatest Common Factor of 429,6877

To find the highest common factor of 429,6877, we have to find the factors of both numbers and list the highest common factor.

The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429

The factors of 6877 are 1, 13, 23, 299, 529, 6877

The HCF of 429,6877 is 13.

Lets's calculate GCF of 429,6877

Greatest Common Factor (GCF) of 429,6877 By Common Division

13	429, 6877
	33, 529

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 429,6877 By Matching Biggest Common Factor Method

Now, list down the factors of 429

1,3,11,13,33,39,143,429

Now, list down the factors of 6877

1,13,23,299,529,6877

Greatest Common Factor

We found the factors 429,6877 . The biggest common factor number is the GCF number.
So the greatest common factor 429,6877 is 13.

Lets's calculate LCM of 174,311

Lowest Common Multiple of 174,311 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 54114

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/54114

Therefore, the GCF of Fractions 429/174,6877/311 is 13/54114

Least Common Multiple of 174,311 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 174,311 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(174,311) = 1

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

GCF(174,311) x common factors =1 x 1 = 1

LCM(174,311) = ( 174 × 311 ) / 1

LCM(174,311) = 54114 / 1

LCM(174,311) = 54114

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FAQs on GCF of Fractions of 429/174, 6877/311

1. What is the HCF of 429,6877?

The HCF of 429,6877 is 13

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 429/174, 6877/311?

Answer: GCF of Numerators as per given numbers 429/174, 6877/311 is

GCF of Numerators i.e. for 429,6877 is 13

LCM of denominators i.e. for 174,311 is 54114.

Thus, GCF of Fractions is 13/54114.Finally, GCF of Fractions for 429/174, 6877/311 is 13/54114.