How to Find GCF of 19/300, 86/118, 538/605?

GCF of 19/300, 86/118, 538/605

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 19/300, 86/118, 538/605 i.e 1/2141700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 19/300, 86/118, 538/605.

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 19/300,86/118,538/605?

Given fractions are 19/300,86/118,538/605

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 19/300,86/118,538/605, numerators are 19,86,538

Denominators are 300,118,605

The GCF of 19,86,538 is 1 .

LCM of 300,118,605 is 2141700.

The greatest common factor of 19/300,86/118,538/605 = [GCF of 19,86,538]/[LCM of 300,118,605]= 1/2141700

Therefore, the GCF of 19/300,86/118,538/605 is 1/2141700.

Greatest Common Factor of 19,86,538

To find the highest common factor of 19,86,538, 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 86 are 1, 2, 43, 86

The factors of 538 are 1, 2, 269, 538

The HCF of 19,86,538 is 1.

Lets's calculate GCF of 19,86,538

Greatest Common Factor (GCF) of 19,86,538 By Common Division

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

Greatest Common Factor of 19,86,538 By Matching Biggest Common Factor Method

Now, list down the factors of 19

1,19

Now, list down the factors of 86

1,2,43,86

Now, list down the factors of 538

1,2,269,538

Greatest Common Factor

We found the factors 19,86,538 . The biggest common factor number is the GCF number.
So the greatest common factor 19,86,538 is 1.

Lets's calculate LCM of 300,118,605

Lowest Common Multiple of 300,118,605 using Common Division

2	300, 118, 605
5	150, 59, 605
	30, 59, 121

∴ So the LCM of the given numbers is 2 x 5 x 30 x 59 x 121 = 2141700

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2141700

Therefore, the GCF of Fractions 19/300,86/118,538/605 is 1/2141700

Least Common Multiple of 300,118,605 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 300,118,605 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(300,118,605) = 1

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

GCF(300,118,605) x common factors =1 x 10 = 10

LCM(300,118,605) = ( 300 × 118 × 605 ) / 10

LCM(300,118,605) = 21417000 / 10

LCM(300,118,605) = 2141700

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FAQs on GCF of Fractions of 19/300, 86/118, 538/605

1. What is the HCF of 19,86,538?

The HCF of 19,86,538 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 19/300, 86/118, 538/605?

Answer: GCF of Numerators as per given numbers 19/300, 86/118, 538/605 is

GCF of Numerators i.e. for 19,86,538 is 1

LCM of denominators i.e. for 300,118,605 is 2141700.

Thus, GCF of Fractions is 1/2141700.Finally, GCF of Fractions for 19/300, 86/118, 538/605 is 1/2141700.