How to Find GCF of 260/314, 8267/9776?

GCF of 260/314, 8267/9776

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 260/314, 8267/9776 i.e 1/1534832 easily. The following is the detailed procedure to determine the greatest common factor of fractions 260/314, 8267/9776.

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 260/314,8267/9776?

Given fractions are 260/314,8267/9776

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 260/314,8267/9776, numerators are 260,8267

Denominators are 314,9776

The GCF of 260,8267 is 1 .

LCM of 314,9776 is 1534832.

The greatest common factor of 260/314,8267/9776 = [GCF of 260,8267]/[LCM of 314,9776]= 1/1534832

Therefore, the GCF of 260/314,8267/9776 is 1/1534832.

Greatest Common Factor of 260,8267

To find the highest common factor of 260,8267, we have to find the factors of both numbers and list the highest common factor.

The factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260

The factors of 8267 are 1, 7, 1181, 8267

The HCF of 260,8267 is 1.

Lets's calculate GCF of 260,8267

Greatest Common Factor (GCF) of 260,8267 By Common Division

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

Greatest Common Factor of 260,8267 By Matching Biggest Common Factor Method

Now, list down the factors of 260

1,2,4,5,10,13,20,26,52,65,130,260

Now, list down the factors of 8267

1,7,1181,8267

Greatest Common Factor

We found the factors 260,8267 . The biggest common factor number is the GCF number.
So the greatest common factor 260,8267 is 1.

Lets's calculate LCM of 314,9776

Lowest Common Multiple of 314,9776 using Common Division

2	314, 9776
	157, 4888

∴ So the LCM of the given numbers is 2 x 157 x 4888 = 1534832

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1534832

Therefore, the GCF of Fractions 260/314,8267/9776 is 1/1534832

Least Common Multiple of 314,9776 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 314,9776 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(314,9776) = 2

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

GCF(314,9776) x common factors =2 x 1 = 2

LCM(314,9776) = ( 314 × 9776 ) / 2

LCM(314,9776) = 3069664 / 2

LCM(314,9776) = 1534832

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FAQs on GCF of Fractions of 260/314, 8267/9776

1. What is the HCF of 260,8267?

The HCF of 260,8267 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 260/314, 8267/9776?

Answer: GCF of Numerators as per given numbers 260/314, 8267/9776 is

GCF of Numerators i.e. for 260,8267 is 1

LCM of denominators i.e. for 314,9776 is 1534832.

Thus, GCF of Fractions is 1/1534832.Finally, GCF of Fractions for 260/314, 8267/9776 is 1/1534832.