How to Find GCF of 421/404, 7722/505?

GCF of 421/404, 7722/505

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 421/404, 7722/505 i.e 1/2020 easily. The following is the detailed procedure to determine the greatest common factor of fractions 421/404, 7722/505.

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 421/404,7722/505?

Given fractions are 421/404,7722/505

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 421/404,7722/505, numerators are 421,7722

Denominators are 404,505

The GCF of 421,7722 is 1 .

LCM of 404,505 is 2020.

The greatest common factor of 421/404,7722/505 = [GCF of 421,7722]/[LCM of 404,505]= 1/2020

Therefore, the GCF of 421/404,7722/505 is 1/2020.

Greatest Common Factor of 421,7722

To find the highest common factor of 421,7722, we have to find the factors of both numbers and list the highest common factor.

The factors of 421 are 1, 421

The factors of 7722 are 1, 2, 3, 6, 9, 11, 13, 18, 22, 26, 27, 33, 39, 54, 66, 78, 99, 117, 143, 198, 234, 286, 297, 351, 429, 594, 702, 858, 1287, 2574, 3861, 7722

The HCF of 421,7722 is 1.

Lets's calculate GCF of 421,7722

Greatest Common Factor (GCF) of 421,7722 By Common Division

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

Greatest Common Factor of 421,7722 By Matching Biggest Common Factor Method

Now, list down the factors of 421

1,421

Now, list down the factors of 7722

1,2,3,6,9,11,13,18,22,26,27,33,39,54,66,78,99,117,143,198,234,286,297,351,429,594,702,858,1287,2574,3861,7722

Greatest Common Factor

We found the factors 421,7722 . The biggest common factor number is the GCF number.
So the greatest common factor 421,7722 is 1.

Lets's calculate LCM of 404,505

Lowest Common Multiple of 404,505 using Common Division

101	404, 505
	4, 5

∴ So the LCM of the given numbers is 101 x 4 x 5 = 2020

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2020

Therefore, the GCF of Fractions 421/404,7722/505 is 1/2020

Least Common Multiple of 404,505 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 404,505 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(404,505) = 101

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

GCF(404,505) x common factors =101 x 1 = 101

LCM(404,505) = ( 404 × 505 ) / 101

LCM(404,505) = 204020 / 101

LCM(404,505) = 2020

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FAQs on GCF of Fractions of 421/404, 7722/505

1. What is the HCF of 421,7722?

The HCF of 421,7722 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 421/404, 7722/505?

Answer: GCF of Numerators as per given numbers 421/404, 7722/505 is

GCF of Numerators i.e. for 421,7722 is 1

LCM of denominators i.e. for 404,505 is 2020.

Thus, GCF of Fractions is 1/2020.Finally, GCF of Fractions for 421/404, 7722/505 is 1/2020.