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GCF of 269/38, 538/164

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 269/38, 538/164 i.e 269/3116 easily. The following is the detailed procedure to determine the greatest common factor of fractions 269/38, 538/164.

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 269/38,538/164?

Given fractions are 269/38,538/164

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 269/38,538/164, numerators are 269,538

Denominators are 38,164

The GCF of 269,538 is 269 .

LCM of 38,164 is 3116.

The greatest common factor of 269/38,538/164 = [GCF of 269,538]/[LCM of 38,164]= 269/3116

Therefore, the GCF of 269/38,538/164 is 269/3116.

Greatest Common Factor of 269,538

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

The factors of 269 are 1, 269

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

The HCF of 269,538 is 269.

Lets's calculate GCF of 269,538

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

269 269, 538
1, 2

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

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

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

Now, list down the factors of 269

:

1,269

Now, list down the factors of 538

:

1,2,269,538

Greatest Common Factor

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

Lets's calculate LCM of 38,164

Lowest Common Multiple of 38,164 using Common Division

2 38, 164
19, 82

∴ So the LCM of the given numbers is 2 x 19 x 82 = 3116

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 269/3116

Therefore, the GCF of Fractions 269/38,538/164 is 269/3116

Least Common Multiple of 38,164 with GCF Formula

Least Common Multiple of 38,164 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 38,164 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(38,164) = 2

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

GCF(38,164) x common factors =2 x 1 = 2

LCM(38,164) = ( 38 × 164 ) / 2

LCM(38,164) = 6232 / 2

LCM(38,164) = 3116


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FAQs on GCF of Fractions of 269/38, 538/164

1. What is the HCF of 269,538?

The HCF of 269,538 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 269/38, 538/164?

Answer: GCF of Numerators as per given numbers 269/38, 538/164 is

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

LCM of denominators i.e. for 38,164 is 3116.

Thus, GCF of Fractions is 269/3116.Finally, GCF of Fractions for 269/38, 538/164 is 269/3116.