How to Find GCF of 214/335, 520/859, 404/189?

GCF of 214/335, 520/859, 404/189

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 214/335, 520/859, 404/189 i.e 2/54387585 easily. The following is the detailed procedure to determine the greatest common factor of fractions 214/335, 520/859, 404/189.

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 214/335,520/859,404/189?

Given fractions are 214/335,520/859,404/189

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 214/335,520/859,404/189, numerators are 214,520,404

Denominators are 335,859,189

The GCF of 214,520,404 is 2 .

LCM of 335,859,189 is 54387585.

The greatest common factor of 214/335,520/859,404/189 = [GCF of 214,520,404]/[LCM of 335,859,189]= 2/54387585

Therefore, the GCF of 214/335,520/859,404/189 is 2/54387585.

Greatest Common Factor of 214,520,404

To find the highest common factor of 214,520,404, we have to find the factors of both numbers and list the highest common factor.

The factors of 214 are 1, 2, 107, 214

The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520

The factors of 404 are 1, 2, 4, 101, 202, 404

The HCF of 214,520,404 is 2.

Lets's calculate GCF of 214,520,404

Greatest Common Factor (GCF) of 214,520,404 By Common Division

2	214, 520, 404
	107, 260, 202

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

Greatest Common Factor of 214,520,404 By Matching Biggest Common Factor Method

Now, list down the factors of 214

1,2,107,214

Now, list down the factors of 520

1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520

Now, list down the factors of 404

1,2,4,101,202,404

Greatest Common Factor

We found the factors 214,520,404 . The biggest common factor number is the GCF number.
So the greatest common factor 214,520,404 is 2.

Lets's calculate LCM of 335,859,189

Lowest Common Multiple of 335,859,189 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 54387585

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/54387585

Therefore, the GCF of Fractions 214/335,520/859,404/189 is 2/54387585

Least Common Multiple of 335,859,189 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 335,859,189 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(335,859,189) = 1

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

GCF(335,859,189) x common factors =1 x 1 = 1

LCM(335,859,189) = ( 335 × 859 × 189 ) / 1

LCM(335,859,189) = 54387585 / 1

LCM(335,859,189) = 54387585

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 214/335, 520/859, 404/189

1. What is the HCF of 214,520,404?

The HCF of 214,520,404 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 214/335, 520/859, 404/189?

Answer: GCF of Numerators as per given numbers 214/335, 520/859, 404/189 is

GCF of Numerators i.e. for 214,520,404 is 2

LCM of denominators i.e. for 335,859,189 is 54387585.

Thus, GCF of Fractions is 2/54387585.Finally, GCF of Fractions for 214/335, 520/859, 404/189 is 2/54387585.