Use our free GCF of Fractions Calculator tool to compute the GCF of 390/213, 305/114 i.e 5/8094 easily. The following is the detailed procedure to determine the greatest common factor of fractions 390/213, 305/114.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 390/213,305/114
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 390/213,305/114, numerators are 390,305
Denominators are 213,114
The GCF of 390,305 is 5 .
LCM of 213,114 is 8094.
The greatest common factor of 390/213,305/114 = [GCF of 390,305]/[LCM of 213,114]= 5/8094
Therefore, the GCF of 390/213,305/114 is 5/8094.
To find the highest common factor of 390,305, we have to find the factors of both numbers and list the highest common factor.
The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
The factors of 305 are 1, 5, 61, 305
The HCF of 390,305 is 5.
Lets's calculate GCF of 390,305
5 | 390, 305 |
78, 61 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 390
:1,2,3,5,6,10,13,15,26,30,39,65,78,130,195,390
Now, list down the factors of 305
:1,5,61,305
Greatest Common Factor
We found the factors 390,305 . The biggest common factor number is the GCF number.
So the greatest common factor 390,305 is 5.
Lets's calculate LCM of 213,114
3 | 213, 114 |
71, 38 |
∴ So the LCM of the given numbers is 3 x 71 x 38 = 8094
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/8094
Therefore, the GCF of Fractions 390/213,305/114 is 5/8094
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 213,114 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(213,114) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(213,114) x common factors =3 x 1 = 3
LCM(213,114) = ( 213 × 114 ) / 3
LCM(213,114) = 24282 / 3
LCM(213,114) = 8094
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 390,305?
The HCF of 390,305 is 5
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 390/213, 305/114?
Answer: GCF of Numerators as per given numbers 390/213, 305/114 is
GCF of Numerators i.e. for 390,305 is 5
LCM of denominators i.e. for 213,114 is 8094.
Thus, GCF of Fractions is 5/8094.Finally, GCF of Fractions for 390/213, 305/114 is 5/8094.