Use our free GCF of Fractions Calculator tool to compute the GCF of 30/581, 30/408, 390/578 i.e 30/4029816 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/581, 30/408, 390/578.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 30/581,30/408,390/578
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 30/581,30/408,390/578, numerators are 30,30,390
Denominators are 581,408,578
The GCF of 30,30,390 is 30 .
LCM of 581,408,578 is 4029816.
The greatest common factor of 30/581,30/408,390/578 = [GCF of 30,30,390]/[LCM of 581,408,578]= 30/4029816
Therefore, the GCF of 30/581,30/408,390/578 is 30/4029816.
To find the highest common factor of 30,30,390, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
The HCF of 30,30,390 is 30.
Lets's calculate GCF of 30,30,390
2 | 30, 30, 390 |
3 | 15, 15, 195 |
5 | 5, 5, 65 |
1, 1, 13 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 390
:1,2,3,5,6,10,13,15,26,30,39,65,78,130,195,390
Greatest Common Factor
We found the factors 30,30,390 . The biggest common factor number is the GCF number.
So the greatest common factor 30,30,390 is 30.
Lets's calculate LCM of 581,408,578
2 | 581, 408, 578 |
17 | 581, 204, 289 |
581, 12, 17 |
∴ So the LCM of the given numbers is 2 x 17 x 581 x 12 x 17 = 4029816
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/4029816
Therefore, the GCF of Fractions 30/581,30/408,390/578 is 30/4029816
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 581,408,578 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(581,408,578) = 1
common factors(in case of two or more numbers have common factors) = 34
GCF(581,408,578) x common factors =1 x 34 = 34
LCM(581,408,578) = ( 581 × 408 × 578 ) / 34
LCM(581,408,578) = 137013744 / 34
LCM(581,408,578) = 4029816
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 30,30,390?
The HCF of 30,30,390 is 30
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 30/581, 30/408, 390/578?
Answer: GCF of Numerators as per given numbers 30/581, 30/408, 390/578 is
GCF of Numerators i.e. for 30,30,390 is 30
LCM of denominators i.e. for 581,408,578 is 4029816.
Thus, GCF of Fractions is 30/4029816.Finally, GCF of Fractions for 30/581, 30/408, 390/578 is 30/4029816.