How to Find GCF of 300/78, 199/3728?

GCF of 300/78, 199/3728

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 300/78, 199/3728 i.e 1/145392 easily. The following is the detailed procedure to determine the greatest common factor of fractions 300/78, 199/3728.

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 300/78,199/3728?

Given fractions are 300/78,199/3728

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 300/78,199/3728, numerators are 300,199

Denominators are 78,3728

The GCF of 300,199 is 1 .

LCM of 78,3728 is 145392.

The greatest common factor of 300/78,199/3728 = [GCF of 300,199]/[LCM of 78,3728]= 1/145392

Therefore, the GCF of 300/78,199/3728 is 1/145392.

Greatest Common Factor of 300,199

To find the highest common factor of 300,199, we have to find the factors of both numbers and list the highest common factor.

The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300

The factors of 199 are 1, 199

The HCF of 300,199 is 1.

Lets's calculate GCF of 300,199

Greatest Common Factor (GCF) of 300,199 By Common Division

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

Greatest Common Factor of 300,199 By Matching Biggest Common Factor Method

Now, list down the factors of 300

1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300

Now, list down the factors of 199

1,199

Greatest Common Factor

We found the factors 300,199 . The biggest common factor number is the GCF number.
So the greatest common factor 300,199 is 1.

Lets's calculate LCM of 78,3728

Lowest Common Multiple of 78,3728 using Common Division

2	78, 3728
	39, 1864

∴ So the LCM of the given numbers is 2 x 39 x 1864 = 145392

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/145392

Therefore, the GCF of Fractions 300/78,199/3728 is 1/145392

Least Common Multiple of 78,3728 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 78,3728 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,3728) = 2

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

GCF(78,3728) x common factors =2 x 1 = 2

LCM(78,3728) = ( 78 × 3728 ) / 2

LCM(78,3728) = 290784 / 2

LCM(78,3728) = 145392

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FAQs on GCF of Fractions of 300/78, 199/3728

1. What is the HCF of 300,199?

The HCF of 300,199 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 300/78, 199/3728?

Answer: GCF of Numerators as per given numbers 300/78, 199/3728 is

GCF of Numerators i.e. for 300,199 is 1

LCM of denominators i.e. for 78,3728 is 145392.

Thus, GCF of Fractions is 1/145392.Finally, GCF of Fractions for 300/78, 199/3728 is 1/145392.