How to Find GCF of 1311/680, 6821/8351?

GCF of 1311/680, 6821/8351

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 1311/680, 6821/8351 i.e 19/5678680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1311/680, 6821/8351.

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 1311/680,6821/8351?

Given fractions are 1311/680,6821/8351

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 1311/680,6821/8351, numerators are 1311,6821

Denominators are 680,8351

The GCF of 1311,6821 is 19 .

LCM of 680,8351 is 5678680.

The greatest common factor of 1311/680,6821/8351 = [GCF of 1311,6821]/[LCM of 680,8351]= 19/5678680

Therefore, the GCF of 1311/680,6821/8351 is 19/5678680.

Greatest Common Factor of 1311,6821

To find the highest common factor of 1311,6821, we have to find the factors of both numbers and list the highest common factor.

The factors of 1311 are 1, 3, 19, 23, 57, 69, 437, 1311

The factors of 6821 are 1, 19, 359, 6821

The HCF of 1311,6821 is 19.

Lets's calculate GCF of 1311,6821

Greatest Common Factor (GCF) of 1311,6821 By Common Division

19	1311, 6821
	69, 359

∴ So the GCF of the given numbers is 19 = 19

Greatest Common Factor of 1311,6821 By Matching Biggest Common Factor Method

Now, list down the factors of 1311

1,3,19,23,57,69,437,1311

Now, list down the factors of 6821

1,19,359,6821

Greatest Common Factor

We found the factors 1311,6821 . The biggest common factor number is the GCF number.
So the greatest common factor 1311,6821 is 19.

Lets's calculate LCM of 680,8351

Lowest Common Multiple of 680,8351 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 5678680

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/5678680

Therefore, the GCF of Fractions 1311/680,6821/8351 is 19/5678680

Least Common Multiple of 680,8351 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 680,8351 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(680,8351) = 1

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

GCF(680,8351) x common factors =1 x 1 = 1

LCM(680,8351) = ( 680 × 8351 ) / 1

LCM(680,8351) = 5678680 / 1

LCM(680,8351) = 5678680

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FAQs on GCF of Fractions of 1311/680, 6821/8351

1. What is the HCF of 1311,6821?

The HCF of 1311,6821 is 19

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 1311/680, 6821/8351?

Answer: GCF of Numerators as per given numbers 1311/680, 6821/8351 is

GCF of Numerators i.e. for 1311,6821 is 19

LCM of denominators i.e. for 680,8351 is 5678680.

Thus, GCF of Fractions is 19/5678680.Finally, GCF of Fractions for 1311/680, 6821/8351 is 19/5678680.