Use our free GCF of Fractions Calculator tool to compute the GCF of 417/289, 710/119 i.e 1/2023 easily. The following is the detailed procedure to determine the greatest common factor of fractions 417/289, 710/119.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 417/289,710/119
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 417/289,710/119, numerators are 417,710
Denominators are 289,119
The GCF of 417,710 is 1 .
LCM of 289,119 is 2023.
The greatest common factor of 417/289,710/119 = [GCF of 417,710]/[LCM of 289,119]= 1/2023
Therefore, the GCF of 417/289,710/119 is 1/2023.
To find the highest common factor of 417,710, we have to find the factors of both numbers and list the highest common factor.
The factors of 417 are 1, 3, 139, 417
The factors of 710 are 1, 2, 5, 10, 71, 142, 355, 710
The HCF of 417,710 is 1.
Lets's calculate GCF of 417,710
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 417
:1,3,139,417
Now, list down the factors of 710
:1,2,5,10,71,142,355,710
Greatest Common Factor
We found the factors 417,710 . The biggest common factor number is the GCF number.
So the greatest common factor 417,710 is 1.
Lets's calculate LCM of 289,119
17 | 289, 119 |
17, 7 |
∴ So the LCM of the given numbers is 17 x 17 x 7 = 2023
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2023
Therefore, the GCF of Fractions 417/289,710/119 is 1/2023
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 289,119 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(289,119) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(289,119) x common factors =17 x 1 = 17
LCM(289,119) = ( 289 × 119 ) / 17
LCM(289,119) = 34391 / 17
LCM(289,119) = 2023
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 417,710?
The HCF of 417,710 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 417/289, 710/119?
Answer: GCF of Numerators as per given numbers 417/289, 710/119 is
GCF of Numerators i.e. for 417,710 is 1
LCM of denominators i.e. for 289,119 is 2023.
Thus, GCF of Fractions is 1/2023.Finally, GCF of Fractions for 417/289, 710/119 is 1/2023.