GCF of 241/30, 289/6880
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 241/30, 289/6880 i.e 1/20640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 241/30, 289/6880.
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 241/30,289/6880?
Given fractions are 241/30,289/6880
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 241/30,289/6880, numerators are 241,289
Denominators are 30,6880
The GCF of 241,289 is 1 .
LCM of 30,6880 is 20640.
The greatest common factor of 241/30,289/6880 = [GCF of 241,289]/[LCM of 30,6880]= 1/20640
Therefore, the GCF of 241/30,289/6880 is 1/20640.
To find the highest common factor of 241,289, we have to find the factors of both numbers and list the highest common factor.
The factors of 241 are 1, 241
The factors of 289 are 1, 17, 289
The HCF of 241,289 is 1.
Lets's calculate GCF of 241,289
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 241,289 By Matching Biggest Common Factor Method
Now, list down the factors of 241
:1,241
Now, list down the factors of 289
:1,17,289
Greatest Common Factor
We found the factors 241,289 . The biggest common factor number is the GCF number.
So the greatest common factor 241,289 is 1.
Lets's calculate LCM of 30,6880
| 2 | 30, 6880 |
| 5 | 15, 3440 |
| 3, 688 |
∴ So the LCM of the given numbers is 2 x 5 x 3 x 688 = 20640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/20640
Therefore, the GCF of Fractions 241/30,289/6880 is 1/20640
Least Common Multiple of 30,6880 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 30,6880 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,6880) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(30,6880) x common factors =10 x 1 = 10
LCM(30,6880) = ( 30 × 6880 ) / 10
LCM(30,6880) = 206400 / 10
LCM(30,6880) = 20640
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 241/30, 289/6880
1. What is the HCF of 241,289?
The HCF of 241,289 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 241/30, 289/6880?
Answer: GCF of Numerators as per given numbers 241/30, 289/6880 is
GCF of Numerators i.e. for 241,289 is 1
LCM of denominators i.e. for 30,6880 is 20640.
Thus, GCF of Fractions is 1/20640.Finally, GCF of Fractions for 241/30, 289/6880 is 1/20640.