How to Find GCF of 204/687, 1274/987?

GCF of 204/687, 1274/987

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 204/687, 1274/987 i.e 2/226023 easily. The following is the detailed procedure to determine the greatest common factor of fractions 204/687, 1274/987.

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 204/687,1274/987?

Given fractions are 204/687,1274/987

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 204/687,1274/987, numerators are 204,1274

Denominators are 687,987

The GCF of 204,1274 is 2 .

LCM of 687,987 is 226023.

The greatest common factor of 204/687,1274/987 = [GCF of 204,1274]/[LCM of 687,987]= 2/226023

Therefore, the GCF of 204/687,1274/987 is 2/226023.

Greatest Common Factor of 204,1274

To find the highest common factor of 204,1274, 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 1274 are 1, 2, 7, 13, 14, 26, 49, 91, 98, 182, 637, 1274

The HCF of 204,1274 is 2.

Lets's calculate GCF of 204,1274

Greatest Common Factor (GCF) of 204,1274 By Common Division

2	204, 1274
	102, 637

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

Greatest Common Factor of 204,1274 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 1274

1,2,7,13,14,26,49,91,98,182,637,1274

Greatest Common Factor

We found the factors 204,1274 . The biggest common factor number is the GCF number.
So the greatest common factor 204,1274 is 2.

Lets's calculate LCM of 687,987

Lowest Common Multiple of 687,987 using Common Division

3	687, 987
	229, 329

∴ So the LCM of the given numbers is 3 x 229 x 329 = 226023

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/226023

Therefore, the GCF of Fractions 204/687,1274/987 is 2/226023

Least Common Multiple of 687,987 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 687,987 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(687,987) = 3

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

GCF(687,987) x common factors =3 x 1 = 3

LCM(687,987) = ( 687 × 987 ) / 3

LCM(687,987) = 678069 / 3

LCM(687,987) = 226023

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FAQs on GCF of Fractions of 204/687, 1274/987

1. What is the HCF of 204,1274?

The HCF of 204,1274 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 204/687, 1274/987?

Answer: GCF of Numerators as per given numbers 204/687, 1274/987 is

GCF of Numerators i.e. for 204,1274 is 2

LCM of denominators i.e. for 687,987 is 226023.

Thus, GCF of Fractions is 2/226023.Finally, GCF of Fractions for 204/687, 1274/987 is 2/226023.