How to Find GCF of 7826/768, 9692/688?

GCF of 7826/768, 9692/688

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 7826/768, 9692/688 i.e 2/33024 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7826/768, 9692/688.

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 7826/768,9692/688?

Given fractions are 7826/768,9692/688

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 7826/768,9692/688, numerators are 7826,9692

Denominators are 768,688

The GCF of 7826,9692 is 2 .

LCM of 768,688 is 33024.

The greatest common factor of 7826/768,9692/688 = [GCF of 7826,9692]/[LCM of 768,688]= 2/33024

Therefore, the GCF of 7826/768,9692/688 is 2/33024.

Greatest Common Factor of 7826,9692

To find the highest common factor of 7826,9692, we have to find the factors of both numbers and list the highest common factor.

The factors of 7826 are 1, 2, 7, 13, 14, 26, 43, 86, 91, 182, 301, 559, 602, 1118, 3913, 7826

The factors of 9692 are 1, 2, 4, 2423, 4846, 9692

The HCF of 7826,9692 is 2.

Lets's calculate GCF of 7826,9692

Greatest Common Factor (GCF) of 7826,9692 By Common Division

2	7826, 9692
	3913, 4846

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

Greatest Common Factor of 7826,9692 By Matching Biggest Common Factor Method

Now, list down the factors of 7826

1,2,7,13,14,26,43,86,91,182,301,559,602,1118,3913,7826

Now, list down the factors of 9692

1,2,4,2423,4846,9692

Greatest Common Factor

We found the factors 7826,9692 . The biggest common factor number is the GCF number.
So the greatest common factor 7826,9692 is 2.

Lets's calculate LCM of 768,688

Lowest Common Multiple of 768,688 using Common Division

2	768, 688
2	384, 344
2	192, 172
2	96, 86
	48, 43

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 48 x 43 = 33024

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/33024

Therefore, the GCF of Fractions 7826/768,9692/688 is 2/33024

Least Common Multiple of 768,688 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 768,688 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(768,688) = 16

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

GCF(768,688) x common factors =16 x 1 = 16

LCM(768,688) = ( 768 × 688 ) / 16

LCM(768,688) = 528384 / 16

LCM(768,688) = 33024

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FAQs on GCF of Fractions of 7826/768, 9692/688

1. What is the HCF of 7826,9692?

The HCF of 7826,9692 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 7826/768, 9692/688?

Answer: GCF of Numerators as per given numbers 7826/768, 9692/688 is

GCF of Numerators i.e. for 7826,9692 is 2

LCM of denominators i.e. for 768,688 is 33024.

Thus, GCF of Fractions is 2/33024.Finally, GCF of Fractions for 7826/768, 9692/688 is 2/33024.