Use our free GCF of Fractions Calculator tool to compute the GCF of 5/31, 8/30, 3/93, 13/510 i.e 1/15810 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5/31, 8/30, 3/93, 13/510.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 5/31,8/30,3/93,13/510
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 5/31,8/30,3/93,13/510, numerators are 5,8,3,13
Denominators are 31,30,93,510
The GCF of 5,8,3,13 is 1 .
LCM of 31,30,93,510 is 15810.
The greatest common factor of 5/31,8/30,3/93,13/510 = [GCF of 5,8,3,13]/[LCM of 31,30,93,510]= 1/15810
Therefore, the GCF of 5/31,8/30,3/93,13/510 is 1/15810.
To find the highest common factor of 5,8,3,13, we have to find the factors of both numbers and list the highest common factor.
The factors of 5 are 1, 5
The factors of 8 are 1, 2, 4, 8
The factors of 3 are 1, 3
The factors of 13 are 1, 13
The HCF of 5,8,3,13 is 1.
Lets's calculate GCF of 5,8,3,13
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 5
:1,5
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 3
:1,3
Now, list down the factors of 13
:1,13
Greatest Common Factor
We found the factors 5,8,3,13 . The biggest common factor number is the GCF number.
So the greatest common factor 5,8,3,13 is 1.
Lets's calculate LCM of 31,30,93,510
2 | 31, 30, 93, 510 |
3 | 31, 15, 93, 255 |
5 | 31, 5, 31, 85 |
31 | 31, 1, 31, 17 |
1, 1, 1, 17 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 31 x 1 x 1 x 1 x 17 = 15810
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15810
Therefore, the GCF of Fractions 5/31,8/30,3/93,13/510 is 1/15810
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 31,30,93,510 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,30,93,510) = 1
common factors(in case of two or more numbers have common factors) = 2790
GCF(31,30,93,510) x common factors =1 x 2790 = 2790
LCM(31,30,93,510) = ( 31 × 30 × 93 × 510 ) / 2790
LCM(31,30,93,510) = 44109900 / 2790
LCM(31,30,93,510) = 15810
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 5,8,3,13?
The HCF of 5,8,3,13 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 5/31, 8/30, 3/93, 13/510?
Answer: GCF of Numerators as per given numbers 5/31, 8/30, 3/93, 13/510 is
GCF of Numerators i.e. for 5,8,3,13 is 1
LCM of denominators i.e. for 31,30,93,510 is 15810.
Thus, GCF of Fractions is 1/15810.Finally, GCF of Fractions for 5/31, 8/30, 3/93, 13/510 is 1/15810.