Use our free GCF of Fractions Calculator tool to compute the GCF of 217/838, 119/724 i.e 7/303356 easily. The following is the detailed procedure to determine the greatest common factor of fractions 217/838, 119/724.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 217/838,119/724
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 217/838,119/724, numerators are 217,119
Denominators are 838,724
The GCF of 217,119 is 7 .
LCM of 838,724 is 303356.
The greatest common factor of 217/838,119/724 = [GCF of 217,119]/[LCM of 838,724]= 7/303356
Therefore, the GCF of 217/838,119/724 is 7/303356.
To find the highest common factor of 217,119, we have to find the factors of both numbers and list the highest common factor.
The factors of 217 are 1, 7, 31, 217
The factors of 119 are 1, 7, 17, 119
The HCF of 217,119 is 7.
Lets's calculate GCF of 217,119
7 | 217, 119 |
31, 17 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 217
:1,7,31,217
Now, list down the factors of 119
:1,7,17,119
Greatest Common Factor
We found the factors 217,119 . The biggest common factor number is the GCF number.
So the greatest common factor 217,119 is 7.
Lets's calculate LCM of 838,724
2 | 838, 724 |
419, 362 |
∴ So the LCM of the given numbers is 2 x 419 x 362 = 303356
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/303356
Therefore, the GCF of Fractions 217/838,119/724 is 7/303356
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 838,724 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(838,724) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(838,724) x common factors =2 x 1 = 2
LCM(838,724) = ( 838 × 724 ) / 2
LCM(838,724) = 606712 / 2
LCM(838,724) = 303356
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 217,119?
The HCF of 217,119 is 7
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 217/838, 119/724?
Answer: GCF of Numerators as per given numbers 217/838, 119/724 is
GCF of Numerators i.e. for 217,119 is 7
LCM of denominators i.e. for 838,724 is 303356.
Thus, GCF of Fractions is 7/303356.Finally, GCF of Fractions for 217/838, 119/724 is 7/303356.