How to Find GCF of 75/38, 311/89, 598/400?

GCF of 75/38, 311/89, 598/400

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 75/38, 311/89, 598/400 i.e 1/676400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 75/38, 311/89, 598/400.

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 75/38,311/89,598/400?

Given fractions are 75/38,311/89,598/400

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 75/38,311/89,598/400, numerators are 75,311,598

Denominators are 38,89,400

The GCF of 75,311,598 is 1 .

LCM of 38,89,400 is 676400.

The greatest common factor of 75/38,311/89,598/400 = [GCF of 75,311,598]/[LCM of 38,89,400]= 1/676400

Therefore, the GCF of 75/38,311/89,598/400 is 1/676400.

Greatest Common Factor of 75,311,598

To find the highest common factor of 75,311,598, we have to find the factors of both numbers and list the highest common factor.

The factors of 75 are 1, 3, 5, 15, 25, 75

The factors of 311 are 1, 311

The factors of 598 are 1, 2, 13, 23, 26, 46, 299, 598

The HCF of 75,311,598 is 1.

Lets's calculate GCF of 75,311,598

Greatest Common Factor (GCF) of 75,311,598 By Common Division

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

Greatest Common Factor of 75,311,598 By Matching Biggest Common Factor Method

Now, list down the factors of 75

1,3,5,15,25,75

Now, list down the factors of 311

1,311

Now, list down the factors of 598

1,2,13,23,26,46,299,598

Greatest Common Factor

We found the factors 75,311,598 . The biggest common factor number is the GCF number.
So the greatest common factor 75,311,598 is 1.

Lets's calculate LCM of 38,89,400

Lowest Common Multiple of 38,89,400 using Common Division

2	38, 89, 400
	19, 89, 200

∴ So the LCM of the given numbers is 2 x 19 x 89 x 200 = 676400

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/676400

Therefore, the GCF of Fractions 75/38,311/89,598/400 is 1/676400

Least Common Multiple of 38,89,400 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 38,89,400 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(38,89,400) = 1

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

GCF(38,89,400) x common factors =1 x 2 = 2

LCM(38,89,400) = ( 38 × 89 × 400 ) / 2

LCM(38,89,400) = 1352800 / 2

LCM(38,89,400) = 676400

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 75/38, 311/89, 598/400

1. What is the HCF of 75,311,598?

The HCF of 75,311,598 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 75/38, 311/89, 598/400?

Answer: GCF of Numerators as per given numbers 75/38, 311/89, 598/400 is

GCF of Numerators i.e. for 75,311,598 is 1

LCM of denominators i.e. for 38,89,400 is 676400.

Thus, GCF of Fractions is 1/676400.Finally, GCF of Fractions for 75/38, 311/89, 598/400 is 1/676400.