How to Find GCF of 814/479, 219/978?

GCF of 814/479, 219/978

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 814/479, 219/978 i.e 1/468462 easily. The following is the detailed procedure to determine the greatest common factor of fractions 814/479, 219/978.

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 814/479,219/978?

Given fractions are 814/479,219/978

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 814/479,219/978, numerators are 814,219

Denominators are 479,978

The GCF of 814,219 is 1 .

LCM of 479,978 is 468462.

The greatest common factor of 814/479,219/978 = [GCF of 814,219]/[LCM of 479,978]= 1/468462

Therefore, the GCF of 814/479,219/978 is 1/468462.

Greatest Common Factor of 814,219

To find the highest common factor of 814,219, we have to find the factors of both numbers and list the highest common factor.

The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814

The factors of 219 are 1, 3, 73, 219

The HCF of 814,219 is 1.

Lets's calculate GCF of 814,219

Greatest Common Factor (GCF) of 814,219 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 814,219 By Matching Biggest Common Factor Method

Now, list down the factors of 814

1,2,11,22,37,74,407,814

Now, list down the factors of 219

1,3,73,219

Greatest Common Factor

We found the factors 814,219 . The biggest common factor number is the GCF number.
So the greatest common factor 814,219 is 1.

Lets's calculate LCM of 479,978

Lowest Common Multiple of 479,978 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 468462

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/468462

Therefore, the GCF of Fractions 814/479,219/978 is 1/468462

Least Common Multiple of 479,978 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 479,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(479,978) = 1

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

GCF(479,978) x common factors =1 x 1 = 1

LCM(479,978) = ( 479 × 978 ) / 1

LCM(479,978) = 468462 / 1

LCM(479,978) = 468462

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 814/479, 219/978

1. What is the HCF of 814,219?

The HCF of 814,219 is 1

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 814/479, 219/978?

Answer: GCF of Numerators as per given numbers 814/479, 219/978 is

GCF of Numerators i.e. for 814,219 is 1

LCM of denominators i.e. for 479,978 is 468462.

Thus, GCF of Fractions is 1/468462.Finally, GCF of Fractions for 814/479, 219/978 is 1/468462.