How to Find GCF of 6831/314, 1030/9774?

GCF of 6831/314, 1030/9774

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 6831/314, 1030/9774 i.e 1/1534518 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6831/314, 1030/9774.

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 6831/314,1030/9774?

Given fractions are 6831/314,1030/9774

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 6831/314,1030/9774, numerators are 6831,1030

Denominators are 314,9774

The GCF of 6831,1030 is 1 .

LCM of 314,9774 is 1534518.

The greatest common factor of 6831/314,1030/9774 = [GCF of 6831,1030]/[LCM of 314,9774]= 1/1534518

Therefore, the GCF of 6831/314,1030/9774 is 1/1534518.

Greatest Common Factor of 6831,1030

To find the highest common factor of 6831,1030, we have to find the factors of both numbers and list the highest common factor.

The factors of 6831 are 1, 3, 9, 11, 23, 27, 33, 69, 99, 207, 253, 297, 621, 759, 2277, 6831

The factors of 1030 are 1, 2, 5, 10, 103, 206, 515, 1030

The HCF of 6831,1030 is 1.

Lets's calculate GCF of 6831,1030

Greatest Common Factor (GCF) of 6831,1030 By Common Division

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

Greatest Common Factor of 6831,1030 By Matching Biggest Common Factor Method

Now, list down the factors of 6831

1,3,9,11,23,27,33,69,99,207,253,297,621,759,2277,6831

Now, list down the factors of 1030

1,2,5,10,103,206,515,1030

Greatest Common Factor

We found the factors 6831,1030 . The biggest common factor number is the GCF number.
So the greatest common factor 6831,1030 is 1.

Lets's calculate LCM of 314,9774

Lowest Common Multiple of 314,9774 using Common Division

2	314, 9774
	157, 4887

∴ So the LCM of the given numbers is 2 x 157 x 4887 = 1534518

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1534518

Therefore, the GCF of Fractions 6831/314,1030/9774 is 1/1534518

Least Common Multiple of 314,9774 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 314,9774 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(314,9774) = 2

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

GCF(314,9774) x common factors =2 x 1 = 2

LCM(314,9774) = ( 314 × 9774 ) / 2

LCM(314,9774) = 3069036 / 2

LCM(314,9774) = 1534518

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FAQs on GCF of Fractions of 6831/314, 1030/9774

1. What is the HCF of 6831,1030?

The HCF of 6831,1030 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 6831/314, 1030/9774?

Answer: GCF of Numerators as per given numbers 6831/314, 1030/9774 is

GCF of Numerators i.e. for 6831,1030 is 1

LCM of denominators i.e. for 314,9774 is 1534518.

Thus, GCF of Fractions is 1/1534518.Finally, GCF of Fractions for 6831/314, 1030/9774 is 1/1534518.