How to Find GCF of 14/172, 73/419, 993/500?

GCF of 14/172, 73/419, 993/500

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 14/172, 73/419, 993/500 i.e 1/9008500 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/172, 73/419, 993/500.

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 14/172,73/419,993/500?

Given fractions are 14/172,73/419,993/500

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 14/172,73/419,993/500, numerators are 14,73,993

Denominators are 172,419,500

The GCF of 14,73,993 is 1 .

LCM of 172,419,500 is 9008500.

The greatest common factor of 14/172,73/419,993/500 = [GCF of 14,73,993]/[LCM of 172,419,500]= 1/9008500

Therefore, the GCF of 14/172,73/419,993/500 is 1/9008500.

Greatest Common Factor of 14,73,993

To find the highest common factor of 14,73,993, we have to find the factors of both numbers and list the highest common factor.

The factors of 14 are 1, 2, 7, 14

The factors of 73 are 1, 73

The factors of 993 are 1, 3, 331, 993

The HCF of 14,73,993 is 1.

Lets's calculate GCF of 14,73,993

Greatest Common Factor (GCF) of 14,73,993 By Common Division

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

Greatest Common Factor of 14,73,993 By Matching Biggest Common Factor Method

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 73

1,73

Now, list down the factors of 993

1,3,331,993

Greatest Common Factor

We found the factors 14,73,993 . The biggest common factor number is the GCF number.
So the greatest common factor 14,73,993 is 1.

Lets's calculate LCM of 172,419,500

Lowest Common Multiple of 172,419,500 using Common Division

2	172, 419, 500
2	86, 419, 250
	43, 419, 125

∴ So the LCM of the given numbers is 2 x 2 x 43 x 419 x 125 = 9008500

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9008500

Therefore, the GCF of Fractions 14/172,73/419,993/500 is 1/9008500

Least Common Multiple of 172,419,500 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 172,419,500 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(172,419,500) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(172,419,500) x common factors =1 x 4 = 4

LCM(172,419,500) = ( 172 × 419 × 500 ) / 4

LCM(172,419,500) = 36034000 / 4

LCM(172,419,500) = 9008500

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 14/172, 73/419, 993/500

1. What is the HCF of 14,73,993?

The HCF of 14,73,993 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 14/172, 73/419, 993/500?

Answer: GCF of Numerators as per given numbers 14/172, 73/419, 993/500 is

GCF of Numerators i.e. for 14,73,993 is 1

LCM of denominators i.e. for 172,419,500 is 9008500.

Thus, GCF of Fractions is 1/9008500.Finally, GCF of Fractions for 14/172, 73/419, 993/500 is 1/9008500.