How to Find GCF of 19/80, 21/14, 172/473?

GCF of 19/80, 21/14, 172/473

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 19/80, 21/14, 172/473 i.e 1/264880 easily. The following is the detailed procedure to determine the greatest common factor of fractions 19/80, 21/14, 172/473.

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 19/80,21/14,172/473?

Given fractions are 19/80,21/14,172/473

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 19/80,21/14,172/473, numerators are 19,21,172

Denominators are 80,14,473

The GCF of 19,21,172 is 1 .

LCM of 80,14,473 is 264880.

The greatest common factor of 19/80,21/14,172/473 = [GCF of 19,21,172]/[LCM of 80,14,473]= 1/264880

Therefore, the GCF of 19/80,21/14,172/473 is 1/264880.

Greatest Common Factor of 19,21,172

To find the highest common factor of 19,21,172, we have to find the factors of both numbers and list the highest common factor.

The factors of 19 are 1, 19

The factors of 21 are 1, 3, 7, 21

The factors of 172 are 1, 2, 4, 43, 86, 172

The HCF of 19,21,172 is 1.

Lets's calculate GCF of 19,21,172

Greatest Common Factor (GCF) of 19,21,172 By Common Division

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

Greatest Common Factor of 19,21,172 By Matching Biggest Common Factor Method

Now, list down the factors of 19

1,19

Now, list down the factors of 21

1,3,7,21

Now, list down the factors of 172

1,2,4,43,86,172

Greatest Common Factor

We found the factors 19,21,172 . The biggest common factor number is the GCF number.
So the greatest common factor 19,21,172 is 1.

Lets's calculate LCM of 80,14,473

Lowest Common Multiple of 80,14,473 using Common Division

2	80, 14, 473
	40, 7, 473

∴ So the LCM of the given numbers is 2 x 40 x 7 x 473 = 264880

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/264880

Therefore, the GCF of Fractions 19/80,21/14,172/473 is 1/264880

Least Common Multiple of 80,14,473 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 80,14,473 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(80,14,473) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(80,14,473) x common factors =1 x 2 = 2

LCM(80,14,473) = ( 80 × 14 × 473 ) / 2

LCM(80,14,473) = 529760 / 2

LCM(80,14,473) = 264880

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 19/80, 21/14, 172/473

1. What is the HCF of 19,21,172?

The HCF of 19,21,172 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 19/80, 21/14, 172/473?

Answer: GCF of Numerators as per given numbers 19/80, 21/14, 172/473 is

GCF of Numerators i.e. for 19,21,172 is 1

LCM of denominators i.e. for 80,14,473 is 264880.

Thus, GCF of Fractions is 1/264880.Finally, GCF of Fractions for 19/80, 21/14, 172/473 is 1/264880.