How to Find GCF of 7723/600, 5677/568?

GCF of 7723/600, 5677/568

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 7723/600, 5677/568 i.e 1/42600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7723/600, 5677/568.

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 7723/600,5677/568?

Given fractions are 7723/600,5677/568

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 7723/600,5677/568, numerators are 7723,5677

Denominators are 600,568

The GCF of 7723,5677 is 1 .

LCM of 600,568 is 42600.

The greatest common factor of 7723/600,5677/568 = [GCF of 7723,5677]/[LCM of 600,568]= 1/42600

Therefore, the GCF of 7723/600,5677/568 is 1/42600.

Greatest Common Factor of 7723,5677

To find the highest common factor of 7723,5677, we have to find the factors of both numbers and list the highest common factor.

The factors of 7723 are 1, 7723

The factors of 5677 are 1, 7, 811, 5677

The HCF of 7723,5677 is 1.

Lets's calculate GCF of 7723,5677

Greatest Common Factor (GCF) of 7723,5677 By Common Division

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

Greatest Common Factor of 7723,5677 By Matching Biggest Common Factor Method

Now, list down the factors of 7723

1,7723

Now, list down the factors of 5677

1,7,811,5677

Greatest Common Factor

We found the factors 7723,5677 . The biggest common factor number is the GCF number.
So the greatest common factor 7723,5677 is 1.

Lets's calculate LCM of 600,568

Lowest Common Multiple of 600,568 using Common Division

2	600, 568
2	300, 284
2	150, 142
	75, 71

∴ So the LCM of the given numbers is 2 x 2 x 2 x 75 x 71 = 42600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/42600

Therefore, the GCF of Fractions 7723/600,5677/568 is 1/42600

Least Common Multiple of 600,568 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 600,568 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(600,568) = 8

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

GCF(600,568) x common factors =8 x 1 = 8

LCM(600,568) = ( 600 × 568 ) / 8

LCM(600,568) = 340800 / 8

LCM(600,568) = 42600

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FAQs on GCF of Fractions of 7723/600, 5677/568

1. What is the HCF of 7723,5677?

The HCF of 7723,5677 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 7723/600, 5677/568?

Answer: GCF of Numerators as per given numbers 7723/600, 5677/568 is

GCF of Numerators i.e. for 7723,5677 is 1

LCM of denominators i.e. for 600,568 is 42600.

Thus, GCF of Fractions is 1/42600.Finally, GCF of Fractions for 7723/600, 5677/568 is 1/42600.