How to Find GCF of 2909/212, 7114/838?

GCF of 2909/212, 7114/838

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 2909/212, 7114/838 i.e 1/88828 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2909/212, 7114/838.

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 2909/212,7114/838?

Given fractions are 2909/212,7114/838

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 2909/212,7114/838, numerators are 2909,7114

Denominators are 212,838

The GCF of 2909,7114 is 1 .

LCM of 212,838 is 88828.

The greatest common factor of 2909/212,7114/838 = [GCF of 2909,7114]/[LCM of 212,838]= 1/88828

Therefore, the GCF of 2909/212,7114/838 is 1/88828.

Greatest Common Factor of 2909,7114

To find the highest common factor of 2909,7114, we have to find the factors of both numbers and list the highest common factor.

The factors of 2909 are 1, 2909

The factors of 7114 are 1, 2, 3557, 7114

The HCF of 2909,7114 is 1.

Lets's calculate GCF of 2909,7114

Greatest Common Factor (GCF) of 2909,7114 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 2909,7114 By Matching Biggest Common Factor Method

Now, list down the factors of 2909

1,2909

Now, list down the factors of 7114

1,2,3557,7114

Greatest Common Factor

We found the factors 2909,7114 . The biggest common factor number is the GCF number.
So the greatest common factor 2909,7114 is 1.

Lets's calculate LCM of 212,838

Lowest Common Multiple of 212,838 using Common Division

2	212, 838
	106, 419

∴ So the LCM of the given numbers is 2 x 106 x 419 = 88828

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/88828

Therefore, the GCF of Fractions 2909/212,7114/838 is 1/88828

Least Common Multiple of 212,838 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 212,838 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(212,838) = 2

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

GCF(212,838) x common factors =2 x 1 = 2

LCM(212,838) = ( 212 × 838 ) / 2

LCM(212,838) = 177656 / 2

LCM(212,838) = 88828

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FAQs on GCF of Fractions of 2909/212, 7114/838

1. What is the HCF of 2909,7114?

The HCF of 2909,7114 is 1

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 2909/212, 7114/838?

Answer: GCF of Numerators as per given numbers 2909/212, 7114/838 is

GCF of Numerators i.e. for 2909,7114 is 1

LCM of denominators i.e. for 212,838 is 88828.

Thus, GCF of Fractions is 1/88828.Finally, GCF of Fractions for 2909/212, 7114/838 is 1/88828.