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GCF of 538/65, 269/196

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 538/65, 269/196 i.e 269/12740 easily. The following is the detailed procedure to determine the greatest common factor of fractions 538/65, 269/196.

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 538/65,269/196?

Given fractions are 538/65,269/196

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 538/65,269/196, numerators are 538,269

Denominators are 65,196

The GCF of 538,269 is 269 .

LCM of 65,196 is 12740.

The greatest common factor of 538/65,269/196 = [GCF of 538,269]/[LCM of 65,196]= 269/12740

Therefore, the GCF of 538/65,269/196 is 269/12740.

Greatest Common Factor of 538,269

To find the highest common factor of 538,269, we have to find the factors of both numbers and list the highest common factor.

The factors of 538 are 1, 2, 269, 538

The factors of 269 are 1, 269

The HCF of 538,269 is 269.

Lets's calculate GCF of 538,269

Greatest Common Factor (GCF) of 538,269 By Common Division

269 538, 269
2, 1

∴ So the GCF of the given numbers is 269 = 269

Greatest Common Factor of 538,269 By Matching Biggest Common Factor Method

Greatest Common Factor of 538,269 By Matching Biggest Common Factor Method

Now, list down the factors of 538

:

1,2,269,538

Now, list down the factors of 269

:

1,269

Greatest Common Factor

We found the factors 538,269 . The biggest common factor number is the GCF number.
So the greatest common factor 538,269 is 269.

Lets's calculate LCM of 65,196

Lowest Common Multiple of 65,196 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 12740

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 269/12740

Therefore, the GCF of Fractions 538/65,269/196 is 269/12740

Least Common Multiple of 65,196 with GCF Formula

Least Common Multiple of 65,196 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 65,196 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,196) = 1

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

GCF(65,196) x common factors =1 x 1 = 1

LCM(65,196) = ( 65 × 196 ) / 1

LCM(65,196) = 12740 / 1

LCM(65,196) = 12740


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FAQs on GCF of Fractions of 538/65, 269/196

1. What is the HCF of 538,269?

The HCF of 538,269 is 269

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 538/65, 269/196?

Answer: GCF of Numerators as per given numbers 538/65, 269/196 is

GCF of Numerators i.e. for 538,269 is 269

LCM of denominators i.e. for 65,196 is 12740.

Thus, GCF of Fractions is 269/12740.Finally, GCF of Fractions for 538/65, 269/196 is 269/12740.