How to Find GCF of 8378/768, 7583/6819?

GCF of 8378/768, 7583/6819

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 8378/768, 7583/6819 i.e 1/1745664 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8378/768, 7583/6819.

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 8378/768,7583/6819?

Given fractions are 8378/768,7583/6819

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 8378/768,7583/6819, numerators are 8378,7583

Denominators are 768,6819

The GCF of 8378,7583 is 1 .

LCM of 768,6819 is 1745664.

The greatest common factor of 8378/768,7583/6819 = [GCF of 8378,7583]/[LCM of 768,6819]= 1/1745664

Therefore, the GCF of 8378/768,7583/6819 is 1/1745664.

Greatest Common Factor of 8378,7583

To find the highest common factor of 8378,7583, we have to find the factors of both numbers and list the highest common factor.

The factors of 8378 are 1, 2, 59, 71, 118, 142, 4189, 8378

The factors of 7583 are 1, 7583

The HCF of 8378,7583 is 1.

Lets's calculate GCF of 8378,7583

Greatest Common Factor (GCF) of 8378,7583 By Common Division

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

Greatest Common Factor of 8378,7583 By Matching Biggest Common Factor Method

Now, list down the factors of 8378

1,2,59,71,118,142,4189,8378

Now, list down the factors of 7583

1,7583

Greatest Common Factor

We found the factors 8378,7583 . The biggest common factor number is the GCF number.
So the greatest common factor 8378,7583 is 1.

Lets's calculate LCM of 768,6819

Lowest Common Multiple of 768,6819 using Common Division

3	768, 6819
	256, 2273

∴ So the LCM of the given numbers is 3 x 256 x 2273 = 1745664

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1745664

Therefore, the GCF of Fractions 8378/768,7583/6819 is 1/1745664

Least Common Multiple of 768,6819 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 768,6819 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(768,6819) = 3

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

GCF(768,6819) x common factors =3 x 1 = 3

LCM(768,6819) = ( 768 × 6819 ) / 3

LCM(768,6819) = 5236992 / 3

LCM(768,6819) = 1745664

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FAQs on GCF of Fractions of 8378/768, 7583/6819

1. What is the HCF of 8378,7583?

The HCF of 8378,7583 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 8378/768, 7583/6819?

Answer: GCF of Numerators as per given numbers 8378/768, 7583/6819 is

GCF of Numerators i.e. for 8378,7583 is 1

LCM of denominators i.e. for 768,6819 is 1745664.

Thus, GCF of Fractions is 1/1745664.Finally, GCF of Fractions for 8378/768, 7583/6819 is 1/1745664.