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GCF of 461/538, 289/400

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 461/538, 289/400 i.e 1/107600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 461/538, 289/400.

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 461/538,289/400?

Given fractions are 461/538,289/400

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 461/538,289/400, numerators are 461,289

Denominators are 538,400

The GCF of 461,289 is 1 .

LCM of 538,400 is 107600.

The greatest common factor of 461/538,289/400 = [GCF of 461,289]/[LCM of 538,400]= 1/107600

Therefore, the GCF of 461/538,289/400 is 1/107600.

Greatest Common Factor of 461,289

To find the highest common factor of 461,289, we have to find the factors of both numbers and list the highest common factor.

The factors of 461 are 1, 461

The factors of 289 are 1, 17, 289

The HCF of 461,289 is 1.

Lets's calculate GCF of 461,289

Greatest Common Factor (GCF) of 461,289 By Common Division

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

Greatest Common Factor of 461,289 By Matching Biggest Common Factor Method

Greatest Common Factor of 461,289 By Matching Biggest Common Factor Method

Now, list down the factors of 461

:

1,461

Now, list down the factors of 289

:

1,17,289

Greatest Common Factor

We found the factors 461,289 . The biggest common factor number is the GCF number.
So the greatest common factor 461,289 is 1.

Lets's calculate LCM of 538,400

Lowest Common Multiple of 538,400 using Common Division

2 538, 400
269, 200

∴ So the LCM of the given numbers is 2 x 269 x 200 = 107600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/107600

Therefore, the GCF of Fractions 461/538,289/400 is 1/107600

Least Common Multiple of 538,400 with GCF Formula

Least Common Multiple of 538,400 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 538,400 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(538,400) = 2

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

GCF(538,400) x common factors =2 x 1 = 2

LCM(538,400) = ( 538 × 400 ) / 2

LCM(538,400) = 215200 / 2

LCM(538,400) = 107600


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FAQs on GCF of Fractions of 461/538, 289/400

1. What is the HCF of 461,289?

The HCF of 461,289 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 461/538, 289/400?

Answer: GCF of Numerators as per given numbers 461/538, 289/400 is

GCF of Numerators i.e. for 461,289 is 1

LCM of denominators i.e. for 538,400 is 107600.

Thus, GCF of Fractions is 1/107600.Finally, GCF of Fractions for 461/538, 289/400 is 1/107600.