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GCF of 519/467, 354/978

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 519/467, 354/978 i.e 3/456726 easily. The following is the detailed procedure to determine the greatest common factor of fractions 519/467, 354/978.

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 519/467,354/978?

Given fractions are 519/467,354/978

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 519/467,354/978, numerators are 519,354

Denominators are 467,978

The GCF of 519,354 is 3 .

LCM of 467,978 is 456726.

The greatest common factor of 519/467,354/978 = [GCF of 519,354]/[LCM of 467,978]= 3/456726

Therefore, the GCF of 519/467,354/978 is 3/456726.

Greatest Common Factor of 519,354

To find the highest common factor of 519,354, we have to find the factors of both numbers and list the highest common factor.

The factors of 519 are 1, 3, 173, 519

The factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354

The HCF of 519,354 is 3.

Lets's calculate GCF of 519,354

Greatest Common Factor (GCF) of 519,354 By Common Division

3 519, 354
173, 118

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 519,354 By Matching Biggest Common Factor Method

Greatest Common Factor of 519,354 By Matching Biggest Common Factor Method

Now, list down the factors of 519

:

1,3,173,519

Now, list down the factors of 354

:

1,2,3,6,59,118,177,354

Greatest Common Factor

We found the factors 519,354 . The biggest common factor number is the GCF number.
So the greatest common factor 519,354 is 3.

Lets's calculate LCM of 467,978

Lowest Common Multiple of 467,978 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 456726

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/456726

Therefore, the GCF of Fractions 519/467,354/978 is 3/456726

Least Common Multiple of 467,978 with GCF Formula

Least Common Multiple of 467,978 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 467,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(467,978) = 1

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

GCF(467,978) x common factors =1 x 1 = 1

LCM(467,978) = ( 467 × 978 ) / 1

LCM(467,978) = 456726 / 1

LCM(467,978) = 456726


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FAQs on GCF of Fractions of 519/467, 354/978

1. What is the HCF of 519,354?

The HCF of 519,354 is 3

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 519/467, 354/978?

Answer: GCF of Numerators as per given numbers 519/467, 354/978 is

GCF of Numerators i.e. for 519,354 is 3

LCM of denominators i.e. for 467,978 is 456726.

Thus, GCF of Fractions is 3/456726.Finally, GCF of Fractions for 519/467, 354/978 is 3/456726.