Use our free GCF of Fractions Calculator tool to compute the GCF of 819/787, 120/500 i.e 3/393500 easily. The following is the detailed procedure to determine the greatest common factor of fractions 819/787, 120/500.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 819/787,120/500
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 819/787,120/500, numerators are 819,120
Denominators are 787,500
The GCF of 819,120 is 3 .
LCM of 787,500 is 393500.
The greatest common factor of 819/787,120/500 = [GCF of 819,120]/[LCM of 787,500]= 3/393500
Therefore, the GCF of 819/787,120/500 is 3/393500.
To find the highest common factor of 819,120, we have to find the factors of both numbers and list the highest common factor.
The factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 819,120 is 3.
Lets's calculate GCF of 819,120
3 | 819, 120 |
273, 40 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 819
:1,3,7,9,13,21,39,63,91,117,273,819
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 819,120 . The biggest common factor number is the GCF number.
So the greatest common factor 819,120 is 3.
Lets's calculate LCM of 787,500
Given numbers has no common factors except 1. So, there LCM is their product i.e 393500
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/393500
Therefore, the GCF of Fractions 819/787,120/500 is 3/393500
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 787,500 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(787,500) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(787,500) x common factors =1 x 1 = 1
LCM(787,500) = ( 787 × 500 ) / 1
LCM(787,500) = 393500 / 1
LCM(787,500) = 393500
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 819,120?
The HCF of 819,120 is 3
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 819/787, 120/500?
Answer: GCF of Numerators as per given numbers 819/787, 120/500 is
GCF of Numerators i.e. for 819,120 is 3
LCM of denominators i.e. for 787,500 is 393500.
Thus, GCF of Fractions is 3/393500.Finally, GCF of Fractions for 819/787, 120/500 is 3/393500.