How to Find GCF of 559/238, 6799/978?

GCF of 559/238, 6799/978

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 559/238, 6799/978 i.e 13/116382 easily. The following is the detailed procedure to determine the greatest common factor of fractions 559/238, 6799/978.

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 559/238,6799/978?

Given fractions are 559/238,6799/978

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 559/238,6799/978, numerators are 559,6799

Denominators are 238,978

The GCF of 559,6799 is 13 .

LCM of 238,978 is 116382.

The greatest common factor of 559/238,6799/978 = [GCF of 559,6799]/[LCM of 238,978]= 13/116382

Therefore, the GCF of 559/238,6799/978 is 13/116382.

Greatest Common Factor of 559,6799

To find the highest common factor of 559,6799, we have to find the factors of both numbers and list the highest common factor.

The factors of 559 are 1, 13, 43, 559

The factors of 6799 are 1, 13, 523, 6799

The HCF of 559,6799 is 13.

Lets's calculate GCF of 559,6799

Greatest Common Factor (GCF) of 559,6799 By Common Division

13	559, 6799
	43, 523

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 559,6799 By Matching Biggest Common Factor Method

Now, list down the factors of 559

1,13,43,559

Now, list down the factors of 6799

1,13,523,6799

Greatest Common Factor

We found the factors 559,6799 . The biggest common factor number is the GCF number.
So the greatest common factor 559,6799 is 13.

Lets's calculate LCM of 238,978

Lowest Common Multiple of 238,978 using Common Division

2	238, 978
	119, 489

∴ So the LCM of the given numbers is 2 x 119 x 489 = 116382

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/116382

Therefore, the GCF of Fractions 559/238,6799/978 is 13/116382

Least Common Multiple of 238,978 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 238,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(238,978) = 2

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

GCF(238,978) x common factors =2 x 1 = 2

LCM(238,978) = ( 238 × 978 ) / 2

LCM(238,978) = 232764 / 2

LCM(238,978) = 116382

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 559/238, 6799/978

1. What is the HCF of 559,6799?

The HCF of 559,6799 is 13

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 559/238, 6799/978?

Answer: GCF of Numerators as per given numbers 559/238, 6799/978 is

GCF of Numerators i.e. for 559,6799 is 13

LCM of denominators i.e. for 238,978 is 116382.

Thus, GCF of Fractions is 13/116382.Finally, GCF of Fractions for 559/238, 6799/978 is 13/116382.