How to Find GCF of 14/37, 580/17, 475/724?

GCF of 14/37, 580/17, 475/724

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 14/37, 580/17, 475/724 i.e 1/455396 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/37, 580/17, 475/724.

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 14/37,580/17,475/724?

Given fractions are 14/37,580/17,475/724

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 14/37,580/17,475/724, numerators are 14,580,475

Denominators are 37,17,724

The GCF of 14,580,475 is 1 .

LCM of 37,17,724 is 455396.

The greatest common factor of 14/37,580/17,475/724 = [GCF of 14,580,475]/[LCM of 37,17,724]= 1/455396

Therefore, the GCF of 14/37,580/17,475/724 is 1/455396.

Greatest Common Factor of 14,580,475

To find the highest common factor of 14,580,475, 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 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580

The factors of 475 are 1, 5, 19, 25, 95, 475

The HCF of 14,580,475 is 1.

Lets's calculate GCF of 14,580,475

Greatest Common Factor (GCF) of 14,580,475 By Common Division

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

Greatest Common Factor of 14,580,475 By Matching Biggest Common Factor Method

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 580

1,2,4,5,10,20,29,58,116,145,290,580

Now, list down the factors of 475

1,5,19,25,95,475

Greatest Common Factor

We found the factors 14,580,475 . The biggest common factor number is the GCF number.
So the greatest common factor 14,580,475 is 1.

Lets's calculate LCM of 37,17,724

Lowest Common Multiple of 37,17,724 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 455396

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/455396

Therefore, the GCF of Fractions 14/37,580/17,475/724 is 1/455396

Least Common Multiple of 37,17,724 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 37,17,724 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(37,17,724) = 1

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

GCF(37,17,724) x common factors =1 x 1 = 1

LCM(37,17,724) = ( 37 × 17 × 724 ) / 1

LCM(37,17,724) = 455396 / 1

LCM(37,17,724) = 455396

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 14/37, 580/17, 475/724

1. What is the HCF of 14,580,475?

The HCF of 14,580,475 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 14/37, 580/17, 475/724?

Answer: GCF of Numerators as per given numbers 14/37, 580/17, 475/724 is

GCF of Numerators i.e. for 14,580,475 is 1

LCM of denominators i.e. for 37,17,724 is 455396.

Thus, GCF of Fractions is 1/455396.Finally, GCF of Fractions for 14/37, 580/17, 475/724 is 1/455396.