How to Find GCF of 5698/437, 1214/191?

GCF of 5698/437, 1214/191

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 5698/437, 1214/191 i.e 2/83467 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5698/437, 1214/191.

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 5698/437,1214/191?

Given fractions are 5698/437,1214/191

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 5698/437,1214/191, numerators are 5698,1214

Denominators are 437,191

The GCF of 5698,1214 is 2 .

LCM of 437,191 is 83467.

The greatest common factor of 5698/437,1214/191 = [GCF of 5698,1214]/[LCM of 437,191]= 2/83467

Therefore, the GCF of 5698/437,1214/191 is 2/83467.

Greatest Common Factor of 5698,1214

To find the highest common factor of 5698,1214, we have to find the factors of both numbers and list the highest common factor.

The factors of 5698 are 1, 2, 7, 11, 14, 22, 37, 74, 77, 154, 259, 407, 518, 814, 2849, 5698

The factors of 1214 are 1, 2, 607, 1214

The HCF of 5698,1214 is 2.

Lets's calculate GCF of 5698,1214

Greatest Common Factor (GCF) of 5698,1214 By Common Division

2	5698, 1214
	2849, 607

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

Greatest Common Factor of 5698,1214 By Matching Biggest Common Factor Method

Now, list down the factors of 5698

1,2,7,11,14,22,37,74,77,154,259,407,518,814,2849,5698

Now, list down the factors of 1214

1,2,607,1214

Greatest Common Factor

We found the factors 5698,1214 . The biggest common factor number is the GCF number.
So the greatest common factor 5698,1214 is 2.

Lets's calculate LCM of 437,191

Lowest Common Multiple of 437,191 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 83467

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/83467

Therefore, the GCF of Fractions 5698/437,1214/191 is 2/83467

Least Common Multiple of 437,191 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 437,191 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(437,191) = 1

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

GCF(437,191) x common factors =1 x 1 = 1

LCM(437,191) = ( 437 × 191 ) / 1

LCM(437,191) = 83467 / 1

LCM(437,191) = 83467

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FAQs on GCF of Fractions of 5698/437, 1214/191

1. What is the HCF of 5698,1214?

The HCF of 5698,1214 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 5698/437, 1214/191?

Answer: GCF of Numerators as per given numbers 5698/437, 1214/191 is

GCF of Numerators i.e. for 5698,1214 is 2

LCM of denominators i.e. for 437,191 is 83467.

Thus, GCF of Fractions is 2/83467.Finally, GCF of Fractions for 5698/437, 1214/191 is 2/83467.