Use our free GCF of Fractions Calculator tool to compute the GCF of 867/319, 900/390 i.e 3/124410 easily. The following is the detailed procedure to determine the greatest common factor of fractions 867/319, 900/390.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 867/319,900/390
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 867/319,900/390, numerators are 867,900
Denominators are 319,390
The GCF of 867,900 is 3 .
LCM of 319,390 is 124410.
The greatest common factor of 867/319,900/390 = [GCF of 867,900]/[LCM of 319,390]= 3/124410
Therefore, the GCF of 867/319,900/390 is 3/124410.
To find the highest common factor of 867,900, we have to find the factors of both numbers and list the highest common factor.
The factors of 867 are 1, 3, 17, 51, 289, 867
The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
The HCF of 867,900 is 3.
Lets's calculate GCF of 867,900
3 | 867, 900 |
289, 300 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 867
:1,3,17,51,289,867
Now, list down the factors of 900
:1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900
Greatest Common Factor
We found the factors 867,900 . The biggest common factor number is the GCF number.
So the greatest common factor 867,900 is 3.
Lets's calculate LCM of 319,390
Given numbers has no common factors except 1. So, there LCM is their product i.e 124410
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/124410
Therefore, the GCF of Fractions 867/319,900/390 is 3/124410
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 319,390 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(319,390) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(319,390) x common factors =1 x 1 = 1
LCM(319,390) = ( 319 × 390 ) / 1
LCM(319,390) = 124410 / 1
LCM(319,390) = 124410
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 867,900?
The HCF of 867,900 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 867/319, 900/390?
Answer: GCF of Numerators as per given numbers 867/319, 900/390 is
GCF of Numerators i.e. for 867,900 is 3
LCM of denominators i.e. for 319,390 is 124410.
Thus, GCF of Fractions is 3/124410.Finally, GCF of Fractions for 867/319, 900/390 is 3/124410.