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GCF of 654/474, 419/314

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 654/474, 419/314 i.e 1/74418 easily. The following is the detailed procedure to determine the greatest common factor of fractions 654/474, 419/314.

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 654/474,419/314?

Given fractions are 654/474,419/314

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 654/474,419/314, numerators are 654,419

Denominators are 474,314

The GCF of 654,419 is 1 .

LCM of 474,314 is 74418.

The greatest common factor of 654/474,419/314 = [GCF of 654,419]/[LCM of 474,314]= 1/74418

Therefore, the GCF of 654/474,419/314 is 1/74418.

Greatest Common Factor of 654,419

To find the highest common factor of 654,419, we have to find the factors of both numbers and list the highest common factor.

The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654

The factors of 419 are 1, 419

The HCF of 654,419 is 1.

Lets's calculate GCF of 654,419

Greatest Common Factor (GCF) of 654,419 By Common Division

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

Greatest Common Factor of 654,419 By Matching Biggest Common Factor Method

Greatest Common Factor of 654,419 By Matching Biggest Common Factor Method

Now, list down the factors of 654

:

1,2,3,6,109,218,327,654

Now, list down the factors of 419

:

1,419

Greatest Common Factor

We found the factors 654,419 . The biggest common factor number is the GCF number.
So the greatest common factor 654,419 is 1.

Lets's calculate LCM of 474,314

Lowest Common Multiple of 474,314 using Common Division

2 474, 314
237, 157

∴ So the LCM of the given numbers is 2 x 237 x 157 = 74418

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/74418

Therefore, the GCF of Fractions 654/474,419/314 is 1/74418

Least Common Multiple of 474,314 with GCF Formula

Least Common Multiple of 474,314 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 474,314 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(474,314) = 2

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

GCF(474,314) x common factors =2 x 1 = 2

LCM(474,314) = ( 474 × 314 ) / 2

LCM(474,314) = 148836 / 2

LCM(474,314) = 74418


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FAQs on GCF of Fractions of 654/474, 419/314

1. What is the HCF of 654,419?

The HCF of 654,419 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 654/474, 419/314?

Answer: GCF of Numerators as per given numbers 654/474, 419/314 is

GCF of Numerators i.e. for 654,419 is 1

LCM of denominators i.e. for 474,314 is 74418.

Thus, GCF of Fractions is 1/74418.Finally, GCF of Fractions for 654/474, 419/314 is 1/74418.