How to Find GCF of 9640/208, 9764/9867?

GCF of 9640/208, 9764/9867

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 9640/208, 9764/9867 i.e 4/157872 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9640/208, 9764/9867.

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 9640/208,9764/9867?

Given fractions are 9640/208,9764/9867

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 9640/208,9764/9867, numerators are 9640,9764

Denominators are 208,9867

The GCF of 9640,9764 is 4 .

LCM of 208,9867 is 157872.

The greatest common factor of 9640/208,9764/9867 = [GCF of 9640,9764]/[LCM of 208,9867]= 4/157872

Therefore, the GCF of 9640/208,9764/9867 is 4/157872.

Greatest Common Factor of 9640,9764

To find the highest common factor of 9640,9764, we have to find the factors of both numbers and list the highest common factor.

The factors of 9640 are 1, 2, 4, 5, 8, 10, 20, 40, 241, 482, 964, 1205, 1928, 2410, 4820, 9640

The factors of 9764 are 1, 2, 4, 2441, 4882, 9764

The HCF of 9640,9764 is 4.

Lets's calculate GCF of 9640,9764

Greatest Common Factor (GCF) of 9640,9764 By Common Division

2	9640, 9764
2	4820, 4882
	2410, 2441

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 9640,9764 By Matching Biggest Common Factor Method

Now, list down the factors of 9640

1,2,4,5,8,10,20,40,241,482,964,1205,1928,2410,4820,9640

Now, list down the factors of 9764

1,2,4,2441,4882,9764

Greatest Common Factor

We found the factors 9640,9764 . The biggest common factor number is the GCF number.
So the greatest common factor 9640,9764 is 4.

Lets's calculate LCM of 208,9867

Lowest Common Multiple of 208,9867 using Common Division

13	208, 9867
	16, 759

∴ So the LCM of the given numbers is 13 x 16 x 759 = 157872

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/157872

Therefore, the GCF of Fractions 9640/208,9764/9867 is 4/157872

Least Common Multiple of 208,9867 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 208,9867 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(208,9867) = 13

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

GCF(208,9867) x common factors =13 x 1 = 13

LCM(208,9867) = ( 208 × 9867 ) / 13

LCM(208,9867) = 2052336 / 13

LCM(208,9867) = 157872

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FAQs on GCF of Fractions of 9640/208, 9764/9867

1. What is the HCF of 9640,9764?

The HCF of 9640,9764 is 4

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 9640/208, 9764/9867?

Answer: GCF of Numerators as per given numbers 9640/208, 9764/9867 is

GCF of Numerators i.e. for 9640,9764 is 4

LCM of denominators i.e. for 208,9867 is 157872.

Thus, GCF of Fractions is 4/157872.Finally, GCF of Fractions for 9640/208, 9764/9867 is 4/157872.