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GCF of 204/616, 493/820

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 204/616, 493/820 i.e 17/126280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 204/616, 493/820.

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 204/616,493/820?

Given fractions are 204/616,493/820

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 204/616,493/820, numerators are 204,493

Denominators are 616,820

The GCF of 204,493 is 17 .

LCM of 616,820 is 126280.

The greatest common factor of 204/616,493/820 = [GCF of 204,493]/[LCM of 616,820]= 17/126280

Therefore, the GCF of 204/616,493/820 is 17/126280.

Greatest Common Factor of 204,493

To find the highest common factor of 204,493, 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 493 are 1, 17, 29, 493

The HCF of 204,493 is 17.

Lets's calculate GCF of 204,493

Greatest Common Factor (GCF) of 204,493 By Common Division

17 204, 493
12, 29

∴ So the GCF of the given numbers is 17 = 17

Greatest Common Factor of 204,493 By Matching Biggest Common Factor Method

Greatest Common Factor of 204,493 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 493

:

1,17,29,493

Greatest Common Factor

We found the factors 204,493 . The biggest common factor number is the GCF number.
So the greatest common factor 204,493 is 17.

Lets's calculate LCM of 616,820

Lowest Common Multiple of 616,820 using Common Division

2 616, 820
2 308, 410
154, 205

∴ So the LCM of the given numbers is 2 x 2 x 154 x 205 = 126280

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/126280

Therefore, the GCF of Fractions 204/616,493/820 is 17/126280

Least Common Multiple of 616,820 with GCF Formula

Least Common Multiple of 616,820 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 616,820 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(616,820) = 4

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

GCF(616,820) x common factors =4 x 1 = 4

LCM(616,820) = ( 616 × 820 ) / 4

LCM(616,820) = 505120 / 4

LCM(616,820) = 126280


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FAQs on GCF of Fractions of 204/616, 493/820

1. What is the HCF of 204,493?

The HCF of 204,493 is 17

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 204/616, 493/820?

Answer: GCF of Numerators as per given numbers 204/616, 493/820 is

GCF of Numerators i.e. for 204,493 is 17

LCM of denominators i.e. for 616,820 is 126280.

Thus, GCF of Fractions is 17/126280.Finally, GCF of Fractions for 204/616, 493/820 is 17/126280.