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GCF of 196/65, 214/183

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 196/65, 214/183 i.e 2/11895 easily. The following is the detailed procedure to determine the greatest common factor of fractions 196/65, 214/183.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 196/65,214/183?

Given fractions are 196/65,214/183

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 196/65,214/183, numerators are 196,214

Denominators are 65,183

The GCF of 196,214 is 2 .

LCM of 65,183 is 11895.

The greatest common factor of 196/65,214/183 = [GCF of 196,214]/[LCM of 65,183]= 2/11895

Therefore, the GCF of 196/65,214/183 is 2/11895.

Greatest Common Factor of 196,214

To find the highest common factor of 196,214, we have to find the factors of both numbers and list the highest common factor.

The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196

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

The HCF of 196,214 is 2.

Lets's calculate GCF of 196,214

Greatest Common Factor (GCF) of 196,214 By Common Division

2 196, 214
98, 107

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

Greatest Common Factor of 196,214 By Matching Biggest Common Factor Method

Greatest Common Factor of 196,214 By Matching Biggest Common Factor Method

Now, list down the factors of 196

:

1,2,4,7,14,28,49,98,196

Now, list down the factors of 214

:

1,2,107,214

Greatest Common Factor

We found the factors 196,214 . The biggest common factor number is the GCF number.
So the greatest common factor 196,214 is 2.

Lets's calculate LCM of 65,183

Lowest Common Multiple of 65,183 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 11895

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/11895

Therefore, the GCF of Fractions 196/65,214/183 is 2/11895

Least Common Multiple of 65,183 with GCF Formula

Least Common Multiple of 65,183 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 65,183 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,183) = 1

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

GCF(65,183) x common factors =1 x 1 = 1

LCM(65,183) = ( 65 × 183 ) / 1

LCM(65,183) = 11895 / 1

LCM(65,183) = 11895


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FAQs on GCF of Fractions of 196/65, 214/183

1. What is the HCF of 196,214?

The HCF of 196,214 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 196/65, 214/183?

Answer: GCF of Numerators as per given numbers 196/65, 214/183 is

GCF of Numerators i.e. for 196,214 is 2

LCM of denominators i.e. for 65,183 is 11895.

Thus, GCF of Fractions is 2/11895.Finally, GCF of Fractions for 196/65, 214/183 is 2/11895.