How to Find GCF of 422/276, 6698/3174?

GCF of 422/276, 6698/3174

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 422/276, 6698/3174 i.e 2/6348 easily. The following is the detailed procedure to determine the greatest common factor of fractions 422/276, 6698/3174.

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 422/276,6698/3174?

Given fractions are 422/276,6698/3174

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 422/276,6698/3174, numerators are 422,6698

Denominators are 276,3174

The GCF of 422,6698 is 2 .

LCM of 276,3174 is 6348.

The greatest common factor of 422/276,6698/3174 = [GCF of 422,6698]/[LCM of 276,3174]= 2/6348

Therefore, the GCF of 422/276,6698/3174 is 2/6348.

Greatest Common Factor of 422,6698

To find the highest common factor of 422,6698, we have to find the factors of both numbers and list the highest common factor.

The factors of 422 are 1, 2, 211, 422

The factors of 6698 are 1, 2, 17, 34, 197, 394, 3349, 6698

The HCF of 422,6698 is 2.

Lets's calculate GCF of 422,6698

Greatest Common Factor (GCF) of 422,6698 By Common Division

2	422, 6698
	211, 3349

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

Greatest Common Factor of 422,6698 By Matching Biggest Common Factor Method

Now, list down the factors of 422

1,2,211,422

Now, list down the factors of 6698

1,2,17,34,197,394,3349,6698

Greatest Common Factor

We found the factors 422,6698 . The biggest common factor number is the GCF number.
So the greatest common factor 422,6698 is 2.

Lets's calculate LCM of 276,3174

Lowest Common Multiple of 276,3174 using Common Division

2	276, 3174
3	138, 1587
23	46, 529
	2, 23

∴ So the LCM of the given numbers is 2 x 3 x 23 x 2 x 23 = 6348

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/6348

Therefore, the GCF of Fractions 422/276,6698/3174 is 2/6348

Least Common Multiple of 276,3174 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 276,3174 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(276,3174) = 138

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

GCF(276,3174) x common factors =138 x 1 = 138

LCM(276,3174) = ( 276 × 3174 ) / 138

LCM(276,3174) = 876024 / 138

LCM(276,3174) = 6348

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FAQs on GCF of Fractions of 422/276, 6698/3174

1. What is the HCF of 422,6698?

The HCF of 422,6698 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 422/276, 6698/3174?

Answer: GCF of Numerators as per given numbers 422/276, 6698/3174 is

GCF of Numerators i.e. for 422,6698 is 2

LCM of denominators i.e. for 276,3174 is 6348.

Thus, GCF of Fractions is 2/6348.Finally, GCF of Fractions for 422/276, 6698/3174 is 2/6348.