How to Find GCF of 214/404, 7111/202?

GCF of 214/404, 7111/202

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 214/404, 7111/202 i.e 1/404 easily. The following is the detailed procedure to determine the greatest common factor of fractions 214/404, 7111/202.

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 214/404,7111/202?

Given fractions are 214/404,7111/202

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 214/404,7111/202, numerators are 214,7111

Denominators are 404,202

The GCF of 214,7111 is 1 .

LCM of 404,202 is 404.

The greatest common factor of 214/404,7111/202 = [GCF of 214,7111]/[LCM of 404,202]= 1/404

Therefore, the GCF of 214/404,7111/202 is 1/404.

Greatest Common Factor of 214,7111

To find the highest common factor of 214,7111, we have to find the factors of both numbers and list the highest common factor.

The factors of 214 are 1, 2, 107, 214

The factors of 7111 are 1, 13, 547, 7111

The HCF of 214,7111 is 1.

Lets's calculate GCF of 214,7111

Greatest Common Factor (GCF) of 214,7111 By Common Division

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

Greatest Common Factor of 214,7111 By Matching Biggest Common Factor Method

Now, list down the factors of 214

1,2,107,214

Now, list down the factors of 7111

1,13,547,7111

Greatest Common Factor

We found the factors 214,7111 . The biggest common factor number is the GCF number.
So the greatest common factor 214,7111 is 1.

Lets's calculate LCM of 404,202

Lowest Common Multiple of 404,202 using Common Division

2	404, 202
101	202, 101
	2, 1

∴ So the LCM of the given numbers is 2 x 101 x 2 x 1 = 404

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/404

Therefore, the GCF of Fractions 214/404,7111/202 is 1/404

Least Common Multiple of 404,202 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 404,202 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(404,202) = 202

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

GCF(404,202) x common factors =202 x 1 = 202

LCM(404,202) = ( 404 × 202 ) / 202

LCM(404,202) = 81608 / 202

LCM(404,202) = 404

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FAQs on GCF of Fractions of 214/404, 7111/202

1. What is the HCF of 214,7111?

The HCF of 214,7111 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 214/404, 7111/202?

Answer: GCF of Numerators as per given numbers 214/404, 7111/202 is

GCF of Numerators i.e. for 214,7111 is 1

LCM of denominators i.e. for 404,202 is 404.

Thus, GCF of Fractions is 1/404.Finally, GCF of Fractions for 214/404, 7111/202 is 1/404.