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GCF of 204/661, 224/287

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 204/661, 224/287 i.e 4/189707 easily. The following is the detailed procedure to determine the greatest common factor of fractions 204/661, 224/287.

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 204/661,224/287?

Given fractions are 204/661,224/287

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 204/661,224/287, numerators are 204,224

Denominators are 661,287

The GCF of 204,224 is 4 .

LCM of 661,287 is 189707.

The greatest common factor of 204/661,224/287 = [GCF of 204,224]/[LCM of 661,287]= 4/189707

Therefore, the GCF of 204/661,224/287 is 4/189707.

Greatest Common Factor of 204,224

To find the highest common factor of 204,224, we have to find the factors of both numbers and list the highest common factor.

The factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204

The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224

The HCF of 204,224 is 4.

Lets's calculate GCF of 204,224

Greatest Common Factor (GCF) of 204,224 By Common Division

2 204, 224
2 102, 112
51, 56

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 204,224 By Matching Biggest Common Factor Method

Greatest Common Factor of 204,224 By Matching Biggest Common Factor Method

Now, list down the factors of 204

:

1,2,3,4,6,12,17,34,51,68,102,204

Now, list down the factors of 224

:

1,2,4,7,8,14,16,28,32,56,112,224

Greatest Common Factor

We found the factors 204,224 . The biggest common factor number is the GCF number.
So the greatest common factor 204,224 is 4.

Lets's calculate LCM of 661,287

Lowest Common Multiple of 661,287 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 189707

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/189707

Therefore, the GCF of Fractions 204/661,224/287 is 4/189707

Least Common Multiple of 661,287 with GCF Formula

Least Common Multiple of 661,287 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 661,287 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(661,287) = 1

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

GCF(661,287) x common factors =1 x 1 = 1

LCM(661,287) = ( 661 × 287 ) / 1

LCM(661,287) = 189707 / 1

LCM(661,287) = 189707


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FAQs on GCF of Fractions of 204/661, 224/287

1. What is the HCF of 204,224?

The HCF of 204,224 is 4

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 204/661, 224/287?

Answer: GCF of Numerators as per given numbers 204/661, 224/287 is

GCF of Numerators i.e. for 204,224 is 4

LCM of denominators i.e. for 661,287 is 189707.

Thus, GCF of Fractions is 4/189707.Finally, GCF of Fractions for 204/661, 224/287 is 4/189707.