Greatest Common Factor of 834/42, 204/51, 864/189

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 834/42, 204/51, 864/189

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

Greatest Common Factor of 834/42,204/51,864/189

Given fractions are 834/42,204/51,864/189

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 834,204,864

Greatest Common Factor of Numerators i.e. GCF of 834,204,864 is 6 .

LCM of Denominators means LCM of 42,51,189 as per the given fractions.

LCM of 42,51,189 is 6426 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 834,204,864

GCF of Fractions 834/42,204/51,864/189 is 6/6426

2 834, 204, 864
3 417, 102, 432
139, 34, 144

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

Greatest Common Factor of 834,204,864 By Matching Biggest Common Factor Method

Greatest Common Factor of 834,204,864 By Matching Biggest Common Factor Method

Factors of 834

List of positive integer factors of 834 that divides 834 without a remainder.

1,2,3,6,139,278,417,834

Factors of 204

List of positive integer factors of 204 that divides 204 without a remainder.

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

Factors of 864

List of positive integer factors of 864 that divides 864 without a remainder.

1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864

Greatest Common Factor

We found the factors 834,204,864 . The biggest common factor number is the GCF number.
So the greatest common factor 834,204,864 is 6.

Lets's calculate LCM of 42,51,189

3 42, 51, 189
7 14, 17, 63
2, 17, 9

∴ So the LCM of the given numbers is 3 x 7 x 2 x 17 x 9 = 6426

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/6426

Therefore, the GCF of Fractions 834/42,204/51,864/189 is 6/6426

Least Common Multiple of 42,51,189 with GCF Formula

Least Common Multiple of 42,51,189 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 42,51,189 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,51,189) = 3

common factors(in case of two or more numbers have common factors) = 21

GCF(42,51,189) x common factors =3 x 21 = 63

LCM(42,51,189) = ( 42 × 51 × 189 ) / 63

LCM(42,51,189) = 404838 / 63

LCM(42,51,189) = 6426


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 834/42, 204/51, 864/189

1. 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.

2. What is the GCF of Fractions for 834/42, 204/51, 864/189?

Answer: GCF of Numerators as per given numbers 834/42, 204/51, 864/189 is

GCF of Numerators i.e. for 834,204,864 is 6

LCM of denominators i.e. for 42,51,189 is 6426.

Thus, GCF of Fractions is 6/6426.Finally, GCF of Fractions for 834/42, 204/51, 864/189 is 6/6426.