How to Find GCF of 73/600, 54/670, 108/814?

GCF of 73/600, 54/670, 108/814

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 73/600, 54/670, 108/814 i.e 1/16361400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 73/600, 54/670, 108/814.

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 73/600,54/670,108/814?

Given fractions are 73/600,54/670,108/814

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 73/600,54/670,108/814, numerators are 73,54,108

Denominators are 600,670,814

The GCF of 73,54,108 is 1 .

LCM of 600,670,814 is 16361400.

The greatest common factor of 73/600,54/670,108/814 = [GCF of 73,54,108]/[LCM of 600,670,814]= 1/16361400

Therefore, the GCF of 73/600,54/670,108/814 is 1/16361400.

Greatest Common Factor of 73,54,108

To find the highest common factor of 73,54,108, we have to find the factors of both numbers and list the highest common factor.

The factors of 73 are 1, 73

The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54

The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

The HCF of 73,54,108 is 1.

Lets's calculate GCF of 73,54,108

Greatest Common Factor (GCF) of 73,54,108 By Common Division

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

Greatest Common Factor of 73,54,108 By Matching Biggest Common Factor Method

Now, list down the factors of 73

1,73

Now, list down the factors of 54

1,2,3,6,9,18,27,54

Now, list down the factors of 108

1,2,3,4,6,9,12,18,27,36,54,108

Greatest Common Factor

We found the factors 73,54,108 . The biggest common factor number is the GCF number.
So the greatest common factor 73,54,108 is 1.

Lets's calculate LCM of 600,670,814

Lowest Common Multiple of 600,670,814 using Common Division

2	600, 670, 814
5	300, 335, 407
	60, 67, 407

∴ So the LCM of the given numbers is 2 x 5 x 60 x 67 x 407 = 16361400

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/16361400

Therefore, the GCF of Fractions 73/600,54/670,108/814 is 1/16361400

Least Common Multiple of 600,670,814 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 600,670,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(600,670,814) = 2

common factors(in case of two or more numbers have common factors) = 10

GCF(600,670,814) x common factors =2 x 10 = 20

LCM(600,670,814) = ( 600 × 670 × 814 ) / 20

LCM(600,670,814) = 327228000 / 20

LCM(600,670,814) = 16361400

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 73/600, 54/670, 108/814

1. What is the HCF of 73,54,108?

The HCF of 73,54,108 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 73/600, 54/670, 108/814?

Answer: GCF of Numerators as per given numbers 73/600, 54/670, 108/814 is

GCF of Numerators i.e. for 73,54,108 is 1

LCM of denominators i.e. for 600,670,814 is 16361400.

Thus, GCF of Fractions is 1/16361400.Finally, GCF of Fractions for 73/600, 54/670, 108/814 is 1/16361400.