How to Find GCF of 7724/404, 5653/8922?

GCF of 7724/404, 5653/8922

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 7724/404, 5653/8922 i.e 1/1802244 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7724/404, 5653/8922.

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 7724/404,5653/8922?

Given fractions are 7724/404,5653/8922

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 7724/404,5653/8922, numerators are 7724,5653

Denominators are 404,8922

The GCF of 7724,5653 is 1 .

LCM of 404,8922 is 1802244.

The greatest common factor of 7724/404,5653/8922 = [GCF of 7724,5653]/[LCM of 404,8922]= 1/1802244

Therefore, the GCF of 7724/404,5653/8922 is 1/1802244.

Greatest Common Factor of 7724,5653

To find the highest common factor of 7724,5653, we have to find the factors of both numbers and list the highest common factor.

The factors of 7724 are 1, 2, 4, 1931, 3862, 7724

The factors of 5653 are 1, 5653

The HCF of 7724,5653 is 1.

Lets's calculate GCF of 7724,5653

Greatest Common Factor (GCF) of 7724,5653 By Common Division

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

Greatest Common Factor of 7724,5653 By Matching Biggest Common Factor Method

Now, list down the factors of 7724

1,2,4,1931,3862,7724

Now, list down the factors of 5653

1,5653

Greatest Common Factor

We found the factors 7724,5653 . The biggest common factor number is the GCF number.
So the greatest common factor 7724,5653 is 1.

Lets's calculate LCM of 404,8922

Lowest Common Multiple of 404,8922 using Common Division

2	404, 8922
	202, 4461

∴ So the LCM of the given numbers is 2 x 202 x 4461 = 1802244

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1802244

Therefore, the GCF of Fractions 7724/404,5653/8922 is 1/1802244

Least Common Multiple of 404,8922 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 404,8922 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(404,8922) = 2

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

GCF(404,8922) x common factors =2 x 1 = 2

LCM(404,8922) = ( 404 × 8922 ) / 2

LCM(404,8922) = 3604488 / 2

LCM(404,8922) = 1802244

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FAQs on GCF of Fractions of 7724/404, 5653/8922

1. What is the HCF of 7724,5653?

The HCF of 7724,5653 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 7724/404, 5653/8922?

Answer: GCF of Numerators as per given numbers 7724/404, 5653/8922 is

GCF of Numerators i.e. for 7724,5653 is 1

LCM of denominators i.e. for 404,8922 is 1802244.

Thus, GCF of Fractions is 1/1802244.Finally, GCF of Fractions for 7724/404, 5653/8922 is 1/1802244.