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GCF of 546/66, 461/459

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 546/66, 461/459 i.e 1/10098 easily. The following is the detailed procedure to determine the greatest common factor of fractions 546/66, 461/459.

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 546/66,461/459?

Given fractions are 546/66,461/459

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 546/66,461/459, numerators are 546,461

Denominators are 66,459

The GCF of 546,461 is 1 .

LCM of 66,459 is 10098.

The greatest common factor of 546/66,461/459 = [GCF of 546,461]/[LCM of 66,459]= 1/10098

Therefore, the GCF of 546/66,461/459 is 1/10098.

Greatest Common Factor of 546,461

To find the highest common factor of 546,461, we have to find the factors of both numbers and list the highest common factor.

The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546

The factors of 461 are 1, 461

The HCF of 546,461 is 1.

Lets's calculate GCF of 546,461

Greatest Common Factor (GCF) of 546,461 By Common Division

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

Greatest Common Factor of 546,461 By Matching Biggest Common Factor Method

Greatest Common Factor of 546,461 By Matching Biggest Common Factor Method

Now, list down the factors of 546

:

1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546

Now, list down the factors of 461

:

1,461

Greatest Common Factor

We found the factors 546,461 . The biggest common factor number is the GCF number.
So the greatest common factor 546,461 is 1.

Lets's calculate LCM of 66,459

Lowest Common Multiple of 66,459 using Common Division

3 66, 459
22, 153

∴ So the LCM of the given numbers is 3 x 22 x 153 = 10098

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10098

Therefore, the GCF of Fractions 546/66,461/459 is 1/10098

Least Common Multiple of 66,459 with GCF Formula

Least Common Multiple of 66,459 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 66,459 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(66,459) = 3

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

GCF(66,459) x common factors =3 x 1 = 3

LCM(66,459) = ( 66 × 459 ) / 3

LCM(66,459) = 30294 / 3

LCM(66,459) = 10098


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FAQs on GCF of Fractions of 546/66, 461/459

1. What is the HCF of 546,461?

The HCF of 546,461 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 546/66, 461/459?

Answer: GCF of Numerators as per given numbers 546/66, 461/459 is

GCF of Numerators i.e. for 546,461 is 1

LCM of denominators i.e. for 66,459 is 10098.

Thus, GCF of Fractions is 1/10098.Finally, GCF of Fractions for 546/66, 461/459 is 1/10098.