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GCF of 463/614, 649/904

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 463/614, 649/904 i.e 1/277528 easily. The following is the detailed procedure to determine the greatest common factor of fractions 463/614, 649/904.

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 463/614,649/904?

Given fractions are 463/614,649/904

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 463/614,649/904, numerators are 463,649

Denominators are 614,904

The GCF of 463,649 is 1 .

LCM of 614,904 is 277528.

The greatest common factor of 463/614,649/904 = [GCF of 463,649]/[LCM of 614,904]= 1/277528

Therefore, the GCF of 463/614,649/904 is 1/277528.

Greatest Common Factor of 463,649

To find the highest common factor of 463,649, we have to find the factors of both numbers and list the highest common factor.

The factors of 463 are 1, 463

The factors of 649 are 1, 11, 59, 649

The HCF of 463,649 is 1.

Lets's calculate GCF of 463,649

Greatest Common Factor (GCF) of 463,649 By Common Division

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

Greatest Common Factor of 463,649 By Matching Biggest Common Factor Method

Greatest Common Factor of 463,649 By Matching Biggest Common Factor Method

Now, list down the factors of 463

:

1,463

Now, list down the factors of 649

:

1,11,59,649

Greatest Common Factor

We found the factors 463,649 . The biggest common factor number is the GCF number.
So the greatest common factor 463,649 is 1.

Lets's calculate LCM of 614,904

Lowest Common Multiple of 614,904 using Common Division

2 614, 904
307, 452

∴ So the LCM of the given numbers is 2 x 307 x 452 = 277528

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/277528

Therefore, the GCF of Fractions 463/614,649/904 is 1/277528

Least Common Multiple of 614,904 with GCF Formula

Least Common Multiple of 614,904 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 614,904 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(614,904) = 2

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

GCF(614,904) x common factors =2 x 1 = 2

LCM(614,904) = ( 614 × 904 ) / 2

LCM(614,904) = 555056 / 2

LCM(614,904) = 277528


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FAQs on GCF of Fractions of 463/614, 649/904

1. What is the HCF of 463,649?

The HCF of 463,649 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 463/614, 649/904?

Answer: GCF of Numerators as per given numbers 463/614, 649/904 is

GCF of Numerators i.e. for 463,649 is 1

LCM of denominators i.e. for 614,904 is 277528.

Thus, GCF of Fractions is 1/277528.Finally, GCF of Fractions for 463/614, 649/904 is 1/277528.