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GCF of 564/268, 374/204

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 564/268, 374/204 i.e 2/13668 easily. The following is the detailed procedure to determine the greatest common factor of fractions 564/268, 374/204.

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 564/268,374/204?

Given fractions are 564/268,374/204

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 564/268,374/204, numerators are 564,374

Denominators are 268,204

The GCF of 564,374 is 2 .

LCM of 268,204 is 13668.

The greatest common factor of 564/268,374/204 = [GCF of 564,374]/[LCM of 268,204]= 2/13668

Therefore, the GCF of 564/268,374/204 is 2/13668.

Greatest Common Factor of 564,374

To find the highest common factor of 564,374, we have to find the factors of both numbers and list the highest common factor.

The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564

The factors of 374 are 1, 2, 11, 17, 22, 34, 187, 374

The HCF of 564,374 is 2.

Lets's calculate GCF of 564,374

Greatest Common Factor (GCF) of 564,374 By Common Division

2 564, 374
282, 187

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

Greatest Common Factor of 564,374 By Matching Biggest Common Factor Method

Greatest Common Factor of 564,374 By Matching Biggest Common Factor Method

Now, list down the factors of 564

:

1,2,3,4,6,12,47,94,141,188,282,564

Now, list down the factors of 374

:

1,2,11,17,22,34,187,374

Greatest Common Factor

We found the factors 564,374 . The biggest common factor number is the GCF number.
So the greatest common factor 564,374 is 2.

Lets's calculate LCM of 268,204

Lowest Common Multiple of 268,204 using Common Division

2 268, 204
2 134, 102
67, 51

∴ So the LCM of the given numbers is 2 x 2 x 67 x 51 = 13668

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/13668

Therefore, the GCF of Fractions 564/268,374/204 is 2/13668

Least Common Multiple of 268,204 with GCF Formula

Least Common Multiple of 268,204 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 268,204 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(268,204) = 4

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

GCF(268,204) x common factors =4 x 1 = 4

LCM(268,204) = ( 268 × 204 ) / 4

LCM(268,204) = 54672 / 4

LCM(268,204) = 13668


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FAQs on GCF of Fractions of 564/268, 374/204

1. What is the HCF of 564,374?

The HCF of 564,374 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 564/268, 374/204?

Answer: GCF of Numerators as per given numbers 564/268, 374/204 is

GCF of Numerators i.e. for 564,374 is 2

LCM of denominators i.e. for 268,204 is 13668.

Thus, GCF of Fractions is 2/13668.Finally, GCF of Fractions for 564/268, 374/204 is 2/13668.