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GCF of 465/478, 279/406

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 465/478, 279/406 i.e 93/97034 easily. The following is the detailed procedure to determine the greatest common factor of fractions 465/478, 279/406.

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 465/478,279/406?

Given fractions are 465/478,279/406

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 465/478,279/406, numerators are 465,279

Denominators are 478,406

The GCF of 465,279 is 93 .

LCM of 478,406 is 97034.

The greatest common factor of 465/478,279/406 = [GCF of 465,279]/[LCM of 478,406]= 93/97034

Therefore, the GCF of 465/478,279/406 is 93/97034.

Greatest Common Factor of 465,279

To find the highest common factor of 465,279, we have to find the factors of both numbers and list the highest common factor.

The factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465

The factors of 279 are 1, 3, 9, 31, 93, 279

The HCF of 465,279 is 93.

Lets's calculate GCF of 465,279

Greatest Common Factor (GCF) of 465,279 By Common Division

3 465, 279
31 155, 93
5, 3

∴ So the GCF of the given numbers is 3 x 31 = 93

Greatest Common Factor of 465,279 By Matching Biggest Common Factor Method

Greatest Common Factor of 465,279 By Matching Biggest Common Factor Method

Now, list down the factors of 465

:

1,3,5,15,31,93,155,465

Now, list down the factors of 279

:

1,3,9,31,93,279

Greatest Common Factor

We found the factors 465,279 . The biggest common factor number is the GCF number.
So the greatest common factor 465,279 is 93.

Lets's calculate LCM of 478,406

Lowest Common Multiple of 478,406 using Common Division

2 478, 406
239, 203

∴ So the LCM of the given numbers is 2 x 239 x 203 = 97034

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 93/97034

Therefore, the GCF of Fractions 465/478,279/406 is 93/97034

Least Common Multiple of 478,406 with GCF Formula

Least Common Multiple of 478,406 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 478,406 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(478,406) = 2

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

GCF(478,406) x common factors =2 x 1 = 2

LCM(478,406) = ( 478 × 406 ) / 2

LCM(478,406) = 194068 / 2

LCM(478,406) = 97034


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FAQs on GCF of Fractions of 465/478, 279/406

1. What is the HCF of 465,279?

The HCF of 465,279 is 93

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 465/478, 279/406?

Answer: GCF of Numerators as per given numbers 465/478, 279/406 is

GCF of Numerators i.e. for 465,279 is 93

LCM of denominators i.e. for 478,406 is 97034.

Thus, GCF of Fractions is 93/97034.Finally, GCF of Fractions for 465/478, 279/406 is 93/97034.