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GCF of 327/38, 687/208

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 327/38, 687/208 i.e 3/3952 easily. The following is the detailed procedure to determine the greatest common factor of fractions 327/38, 687/208.

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 327/38,687/208?

Given fractions are 327/38,687/208

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 327/38,687/208, numerators are 327,687

Denominators are 38,208

The GCF of 327,687 is 3 .

LCM of 38,208 is 3952.

The greatest common factor of 327/38,687/208 = [GCF of 327,687]/[LCM of 38,208]= 3/3952

Therefore, the GCF of 327/38,687/208 is 3/3952.

Greatest Common Factor of 327,687

To find the highest common factor of 327,687, we have to find the factors of both numbers and list the highest common factor.

The factors of 327 are 1, 3, 109, 327

The factors of 687 are 1, 3, 229, 687

The HCF of 327,687 is 3.

Lets's calculate GCF of 327,687

Greatest Common Factor (GCF) of 327,687 By Common Division

3 327, 687
109, 229

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 327,687 By Matching Biggest Common Factor Method

Greatest Common Factor of 327,687 By Matching Biggest Common Factor Method

Now, list down the factors of 327

:

1,3,109,327

Now, list down the factors of 687

:

1,3,229,687

Greatest Common Factor

We found the factors 327,687 . The biggest common factor number is the GCF number.
So the greatest common factor 327,687 is 3.

Lets's calculate LCM of 38,208

Lowest Common Multiple of 38,208 using Common Division

2 38, 208
19, 104

∴ So the LCM of the given numbers is 2 x 19 x 104 = 3952

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/3952

Therefore, the GCF of Fractions 327/38,687/208 is 3/3952

Least Common Multiple of 38,208 with GCF Formula

Least Common Multiple of 38,208 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 38,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(38,208) = 2

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

GCF(38,208) x common factors =2 x 1 = 2

LCM(38,208) = ( 38 × 208 ) / 2

LCM(38,208) = 7904 / 2

LCM(38,208) = 3952


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FAQs on GCF of Fractions of 327/38, 687/208

1. What is the HCF of 327,687?

The HCF of 327,687 is 3

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 327/38, 687/208?

Answer: GCF of Numerators as per given numbers 327/38, 687/208 is

GCF of Numerators i.e. for 327,687 is 3

LCM of denominators i.e. for 38,208 is 3952.

Thus, GCF of Fractions is 3/3952.Finally, GCF of Fractions for 327/38, 687/208 is 3/3952.