Use our free GCF of Fractions Calculator tool to compute the GCF of 97/462, 20/510, 809/119 i.e 1/39270 easily. The following is the detailed procedure to determine the greatest common factor of fractions 97/462, 20/510, 809/119.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 97/462,20/510,809/119
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 97/462,20/510,809/119, numerators are 97,20,809
Denominators are 462,510,119
The GCF of 97,20,809 is 1 .
LCM of 462,510,119 is 39270.
The greatest common factor of 97/462,20/510,809/119 = [GCF of 97,20,809]/[LCM of 462,510,119]= 1/39270
Therefore, the GCF of 97/462,20/510,809/119 is 1/39270.
To find the highest common factor of 97,20,809, we have to find the factors of both numbers and list the highest common factor.
The factors of 97 are 1, 97
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 809 are 1, 809
The HCF of 97,20,809 is 1.
Lets's calculate GCF of 97,20,809
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 97
:1,97
Now, list down the factors of 20
:1,2,4,5,10,20
Now, list down the factors of 809
:1,809
Greatest Common Factor
We found the factors 97,20,809 . The biggest common factor number is the GCF number.
So the greatest common factor 97,20,809 is 1.
Lets's calculate LCM of 462,510,119
2 | 462, 510, 119 |
3 | 231, 255, 119 |
7 | 77, 85, 119 |
17 | 11, 85, 17 |
11, 5, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 17 x 11 x 5 x 1 = 39270
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/39270
Therefore, the GCF of Fractions 97/462,20/510,809/119 is 1/39270
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 462,510,119 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(462,510,119) = 1
common factors(in case of two or more numbers have common factors) = 714
GCF(462,510,119) x common factors =1 x 714 = 714
LCM(462,510,119) = ( 462 × 510 × 119 ) / 714
LCM(462,510,119) = 28038780 / 714
LCM(462,510,119) = 39270
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 97,20,809?
The HCF of 97,20,809 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 97/462, 20/510, 809/119?
Answer: GCF of Numerators as per given numbers 97/462, 20/510, 809/119 is
GCF of Numerators i.e. for 97,20,809 is 1
LCM of denominators i.e. for 462,510,119 is 39270.
Thus, GCF of Fractions is 1/39270.Finally, GCF of Fractions for 97/462, 20/510, 809/119 is 1/39270.