How to Find GCF of 3112/219, 9422/686?

GCF of 3112/219, 9422/686

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 3112/219, 9422/686 i.e 2/150234 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3112/219, 9422/686.

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 3112/219,9422/686?

Given fractions are 3112/219,9422/686

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 3112/219,9422/686, numerators are 3112,9422

Denominators are 219,686

The GCF of 3112,9422 is 2 .

LCM of 219,686 is 150234.

The greatest common factor of 3112/219,9422/686 = [GCF of 3112,9422]/[LCM of 219,686]= 2/150234

Therefore, the GCF of 3112/219,9422/686 is 2/150234.

Greatest Common Factor of 3112,9422

To find the highest common factor of 3112,9422, we have to find the factors of both numbers and list the highest common factor.

The factors of 3112 are 1, 2, 4, 8, 389, 778, 1556, 3112

The factors of 9422 are 1, 2, 7, 14, 673, 1346, 4711, 9422

The HCF of 3112,9422 is 2.

Lets's calculate GCF of 3112,9422

Greatest Common Factor (GCF) of 3112,9422 By Common Division

2	3112, 9422
	1556, 4711

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

Greatest Common Factor of 3112,9422 By Matching Biggest Common Factor Method

Now, list down the factors of 3112

1,2,4,8,389,778,1556,3112

Now, list down the factors of 9422

1,2,7,14,673,1346,4711,9422

Greatest Common Factor

We found the factors 3112,9422 . The biggest common factor number is the GCF number.
So the greatest common factor 3112,9422 is 2.

Lets's calculate LCM of 219,686

Lowest Common Multiple of 219,686 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 150234

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/150234

Therefore, the GCF of Fractions 3112/219,9422/686 is 2/150234

Least Common Multiple of 219,686 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 219,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(219,686) = 1

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

GCF(219,686) x common factors =1 x 1 = 1

LCM(219,686) = ( 219 × 686 ) / 1

LCM(219,686) = 150234 / 1

LCM(219,686) = 150234

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FAQs on GCF of Fractions of 3112/219, 9422/686

1. What is the HCF of 3112,9422?

The HCF of 3112,9422 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 3112/219, 9422/686?

Answer: GCF of Numerators as per given numbers 3112/219, 9422/686 is

GCF of Numerators i.e. for 3112,9422 is 2

LCM of denominators i.e. for 219,686 is 150234.

Thus, GCF of Fractions is 2/150234.Finally, GCF of Fractions for 3112/219, 9422/686 is 2/150234.