How to Find GCF of 812/137, 678/873?

GCF of 812/137, 678/873

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 812/137, 678/873 i.e 2/119601 easily. The following is the detailed procedure to determine the greatest common factor of fractions 812/137, 678/873.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 812/137,678/873?

Given fractions are 812/137,678/873

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 812/137,678/873, numerators are 812,678

Denominators are 137,873

The GCF of 812,678 is 2 .

LCM of 137,873 is 119601.

The greatest common factor of 812/137,678/873 = [GCF of 812,678]/[LCM of 137,873]= 2/119601

Therefore, the GCF of 812/137,678/873 is 2/119601.

Greatest Common Factor of 812,678

To find the highest common factor of 812,678, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678

The HCF of 812,678 is 2.

Lets's calculate GCF of 812,678

Greatest Common Factor (GCF) of 812,678 By Common Division

2	812, 678
	406, 339

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 812,678 By Matching Biggest Common Factor Method

Now, list down the factors of 812

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

Now, list down the factors of 678

1,2,3,6,113,226,339,678

Greatest Common Factor

We found the factors 812,678 . The biggest common factor number is the GCF number.
So the greatest common factor 812,678 is 2.

Lets's calculate LCM of 137,873

Lowest Common Multiple of 137,873 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 119601

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/119601

Therefore, the GCF of Fractions 812/137,678/873 is 2/119601

Least Common Multiple of 137,873 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 137,873 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(137,873) = 1

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

GCF(137,873) x common factors =1 x 1 = 1

LCM(137,873) = ( 137 × 873 ) / 1

LCM(137,873) = 119601 / 1

LCM(137,873) = 119601

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FAQs on GCF of Fractions of 812/137, 678/873

1. What is the HCF of 812,678?

The HCF of 812,678 is 2

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 812/137, 678/873?

Answer: GCF of Numerators as per given numbers 812/137, 678/873 is

GCF of Numerators i.e. for 812,678 is 2

LCM of denominators i.e. for 137,873 is 119601.

Thus, GCF of Fractions is 2/119601.Finally, GCF of Fractions for 812/137, 678/873 is 2/119601.