How to Find GCF of 322/404, 7678/389?

GCF of 322/404, 7678/389

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 322/404, 7678/389 i.e 2/157156 easily. The following is the detailed procedure to determine the greatest common factor of fractions 322/404, 7678/389.

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 322/404,7678/389?

Given fractions are 322/404,7678/389

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 322/404,7678/389, numerators are 322,7678

Denominators are 404,389

The GCF of 322,7678 is 2 .

LCM of 404,389 is 157156.

The greatest common factor of 322/404,7678/389 = [GCF of 322,7678]/[LCM of 404,389]= 2/157156

Therefore, the GCF of 322/404,7678/389 is 2/157156.

Greatest Common Factor of 322,7678

To find the highest common factor of 322,7678, we have to find the factors of both numbers and list the highest common factor.

The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322

The factors of 7678 are 1, 2, 11, 22, 349, 698, 3839, 7678

The HCF of 322,7678 is 2.

Lets's calculate GCF of 322,7678

Greatest Common Factor (GCF) of 322,7678 By Common Division

2	322, 7678
	161, 3839

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

Greatest Common Factor of 322,7678 By Matching Biggest Common Factor Method

Now, list down the factors of 322

1,2,7,14,23,46,161,322

Now, list down the factors of 7678

1,2,11,22,349,698,3839,7678

Greatest Common Factor

We found the factors 322,7678 . The biggest common factor number is the GCF number.
So the greatest common factor 322,7678 is 2.

Lets's calculate LCM of 404,389

Lowest Common Multiple of 404,389 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 157156

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/157156

Therefore, the GCF of Fractions 322/404,7678/389 is 2/157156

Least Common Multiple of 404,389 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 404,389 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(404,389) = 1

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

GCF(404,389) x common factors =1 x 1 = 1

LCM(404,389) = ( 404 × 389 ) / 1

LCM(404,389) = 157156 / 1

LCM(404,389) = 157156

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FAQs on GCF of Fractions of 322/404, 7678/389

1. What is the HCF of 322,7678?

The HCF of 322,7678 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 322/404, 7678/389?

Answer: GCF of Numerators as per given numbers 322/404, 7678/389 is

GCF of Numerators i.e. for 322,7678 is 2

LCM of denominators i.e. for 404,389 is 157156.

Thus, GCF of Fractions is 2/157156.Finally, GCF of Fractions for 322/404, 7678/389 is 2/157156.