How to Find GCF of 7706/827, 6850/7961?

GCF of 7706/827, 6850/7961

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 7706/827, 6850/7961 i.e 2/6583747 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7706/827, 6850/7961.

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 7706/827,6850/7961?

Given fractions are 7706/827,6850/7961

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 7706/827,6850/7961, numerators are 7706,6850

Denominators are 827,7961

The GCF of 7706,6850 is 2 .

LCM of 827,7961 is 6583747.

The greatest common factor of 7706/827,6850/7961 = [GCF of 7706,6850]/[LCM of 827,7961]= 2/6583747

Therefore, the GCF of 7706/827,6850/7961 is 2/6583747.

Greatest Common Factor of 7706,6850

To find the highest common factor of 7706,6850, we have to find the factors of both numbers and list the highest common factor.

The factors of 7706 are 1, 2, 3853, 7706

The factors of 6850 are 1, 2, 5, 10, 25, 50, 137, 274, 685, 1370, 3425, 6850

The HCF of 7706,6850 is 2.

Lets's calculate GCF of 7706,6850

Greatest Common Factor (GCF) of 7706,6850 By Common Division

2	7706, 6850
	3853, 3425

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

Greatest Common Factor of 7706,6850 By Matching Biggest Common Factor Method

Now, list down the factors of 7706

1,2,3853,7706

Now, list down the factors of 6850

1,2,5,10,25,50,137,274,685,1370,3425,6850

Greatest Common Factor

We found the factors 7706,6850 . The biggest common factor number is the GCF number.
So the greatest common factor 7706,6850 is 2.

Lets's calculate LCM of 827,7961

Lowest Common Multiple of 827,7961 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 6583747

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/6583747

Therefore, the GCF of Fractions 7706/827,6850/7961 is 2/6583747

Least Common Multiple of 827,7961 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 827,7961 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(827,7961) = 1

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

GCF(827,7961) x common factors =1 x 1 = 1

LCM(827,7961) = ( 827 × 7961 ) / 1

LCM(827,7961) = 6583747 / 1

LCM(827,7961) = 6583747

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FAQs on GCF of Fractions of 7706/827, 6850/7961

1. What is the HCF of 7706,6850?

The HCF of 7706,6850 is 2

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 7706/827, 6850/7961?

Answer: GCF of Numerators as per given numbers 7706/827, 6850/7961 is

GCF of Numerators i.e. for 7706,6850 is 2

LCM of denominators i.e. for 827,7961 is 6583747.

Thus, GCF of Fractions is 2/6583747.Finally, GCF of Fractions for 7706/827, 6850/7961 is 2/6583747.