How to Find GCF of 2004/256, 1938/644?

GCF of 2004/256, 1938/644

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 2004/256, 1938/644 i.e 6/41216 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2004/256, 1938/644.

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 2004/256,1938/644?

Given fractions are 2004/256,1938/644

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 2004/256,1938/644, numerators are 2004,1938

Denominators are 256,644

The GCF of 2004,1938 is 6 .

LCM of 256,644 is 41216.

The greatest common factor of 2004/256,1938/644 = [GCF of 2004,1938]/[LCM of 256,644]= 6/41216

Therefore, the GCF of 2004/256,1938/644 is 6/41216.

Greatest Common Factor of 2004,1938

To find the highest common factor of 2004,1938, we have to find the factors of both numbers and list the highest common factor.

The factors of 2004 are 1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004

The factors of 1938 are 1, 2, 3, 6, 17, 19, 34, 38, 51, 57, 102, 114, 323, 646, 969, 1938

The HCF of 2004,1938 is 6.

Lets's calculate GCF of 2004,1938

Greatest Common Factor (GCF) of 2004,1938 By Common Division

2	2004, 1938
3	1002, 969
	334, 323

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 2004,1938 By Matching Biggest Common Factor Method

Now, list down the factors of 2004

1,2,3,4,6,12,167,334,501,668,1002,2004

Now, list down the factors of 1938

1,2,3,6,17,19,34,38,51,57,102,114,323,646,969,1938

Greatest Common Factor

We found the factors 2004,1938 . The biggest common factor number is the GCF number.
So the greatest common factor 2004,1938 is 6.

Lets's calculate LCM of 256,644

Lowest Common Multiple of 256,644 using Common Division

2	256, 644
2	128, 322
	64, 161

∴ So the LCM of the given numbers is 2 x 2 x 64 x 161 = 41216

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/41216

Therefore, the GCF of Fractions 2004/256,1938/644 is 6/41216

Least Common Multiple of 256,644 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 256,644 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(256,644) = 4

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

GCF(256,644) x common factors =4 x 1 = 4

LCM(256,644) = ( 256 × 644 ) / 4

LCM(256,644) = 164864 / 4

LCM(256,644) = 41216

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 2004/256, 1938/644

1. What is the HCF of 2004,1938?

The HCF of 2004,1938 is 6

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 2004/256, 1938/644?

Answer: GCF of Numerators as per given numbers 2004/256, 1938/644 is

GCF of Numerators i.e. for 2004,1938 is 6

LCM of denominators i.e. for 256,644 is 41216.

Thus, GCF of Fractions is 6/41216.Finally, GCF of Fractions for 2004/256, 1938/644 is 6/41216.