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GCF of 273/205, 812/351

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 273/205, 812/351 i.e 7/71955 easily. The following is the detailed procedure to determine the greatest common factor of fractions 273/205, 812/351.

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 273/205,812/351?

Given fractions are 273/205,812/351

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 273/205,812/351, numerators are 273,812

Denominators are 205,351

The GCF of 273,812 is 7 .

LCM of 205,351 is 71955.

The greatest common factor of 273/205,812/351 = [GCF of 273,812]/[LCM of 205,351]= 7/71955

Therefore, the GCF of 273/205,812/351 is 7/71955.

Greatest Common Factor of 273,812

To find the highest common factor of 273,812, we have to find the factors of both numbers and list the highest common factor.

The factors of 273 are 1, 3, 7, 13, 21, 39, 91, 273

The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812

The HCF of 273,812 is 7.

Lets's calculate GCF of 273,812

Greatest Common Factor (GCF) of 273,812 By Common Division

7 273, 812
39, 116

∴ So the GCF of the given numbers is 7 = 7

Greatest Common Factor of 273,812 By Matching Biggest Common Factor Method

Greatest Common Factor of 273,812 By Matching Biggest Common Factor Method

Now, list down the factors of 273

:

1,3,7,13,21,39,91,273

Now, list down the factors of 812

:

1,2,4,7,14,28,29,58,116,203,406,812

Greatest Common Factor

We found the factors 273,812 . The biggest common factor number is the GCF number.
So the greatest common factor 273,812 is 7.

Lets's calculate LCM of 205,351

Lowest Common Multiple of 205,351 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 71955

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/71955

Therefore, the GCF of Fractions 273/205,812/351 is 7/71955

Least Common Multiple of 205,351 with GCF Formula

Least Common Multiple of 205,351 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 205,351 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(205,351) = 1

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

GCF(205,351) x common factors =1 x 1 = 1

LCM(205,351) = ( 205 × 351 ) / 1

LCM(205,351) = 71955 / 1

LCM(205,351) = 71955


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FAQs on GCF of Fractions of 273/205, 812/351

1. What is the HCF of 273,812?

The HCF of 273,812 is 7

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 273/205, 812/351?

Answer: GCF of Numerators as per given numbers 273/205, 812/351 is

GCF of Numerators i.e. for 273,812 is 7

LCM of denominators i.e. for 205,351 is 71955.

Thus, GCF of Fractions is 7/71955.Finally, GCF of Fractions for 273/205, 812/351 is 7/71955.