How to Find GCF of 9821/228, 6809/7729?

GCF of 9821/228, 6809/7729

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 9821/228, 6809/7729 i.e 1/1762212 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9821/228, 6809/7729.

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 9821/228,6809/7729?

Given fractions are 9821/228,6809/7729

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 9821/228,6809/7729, numerators are 9821,6809

Denominators are 228,7729

The GCF of 9821,6809 is 1 .

LCM of 228,7729 is 1762212.

The greatest common factor of 9821/228,6809/7729 = [GCF of 9821,6809]/[LCM of 228,7729]= 1/1762212

Therefore, the GCF of 9821/228,6809/7729 is 1/1762212.

Greatest Common Factor of 9821,6809

To find the highest common factor of 9821,6809, we have to find the factors of both numbers and list the highest common factor.

The factors of 9821 are 1, 7, 23, 61, 161, 427, 1403, 9821

The factors of 6809 are 1, 11, 619, 6809

The HCF of 9821,6809 is 1.

Lets's calculate GCF of 9821,6809

Greatest Common Factor (GCF) of 9821,6809 By Common Division

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

Greatest Common Factor of 9821,6809 By Matching Biggest Common Factor Method

Now, list down the factors of 9821

1,7,23,61,161,427,1403,9821

Now, list down the factors of 6809

1,11,619,6809

Greatest Common Factor

We found the factors 9821,6809 . The biggest common factor number is the GCF number.
So the greatest common factor 9821,6809 is 1.

Lets's calculate LCM of 228,7729

Lowest Common Multiple of 228,7729 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1762212

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1762212

Therefore, the GCF of Fractions 9821/228,6809/7729 is 1/1762212

Least Common Multiple of 228,7729 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 228,7729 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(228,7729) = 1

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

GCF(228,7729) x common factors =1 x 1 = 1

LCM(228,7729) = ( 228 × 7729 ) / 1

LCM(228,7729) = 1762212 / 1

LCM(228,7729) = 1762212

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FAQs on GCF of Fractions of 9821/228, 6809/7729

1. What is the HCF of 9821,6809?

The HCF of 9821,6809 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 9821/228, 6809/7729?

Answer: GCF of Numerators as per given numbers 9821/228, 6809/7729 is

GCF of Numerators i.e. for 9821,6809 is 1

LCM of denominators i.e. for 228,7729 is 1762212.

Thus, GCF of Fractions is 1/1762212.Finally, GCF of Fractions for 9821/228, 6809/7729 is 1/1762212.