Use our free GCF of Fractions Calculator tool to compute the GCF of 13/218, 53/103, 920/309 i.e 1/67362 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/218, 53/103, 920/309.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 13/218,53/103,920/309
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 13/218,53/103,920/309, numerators are 13,53,920
Denominators are 218,103,309
The GCF of 13,53,920 is 1 .
LCM of 218,103,309 is 67362.
The greatest common factor of 13/218,53/103,920/309 = [GCF of 13,53,920]/[LCM of 218,103,309]= 1/67362
Therefore, the GCF of 13/218,53/103,920/309 is 1/67362.
To find the highest common factor of 13,53,920, we have to find the factors of both numbers and list the highest common factor.
The factors of 13 are 1, 13
The factors of 53 are 1, 53
The factors of 920 are 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920
The HCF of 13,53,920 is 1.
Lets's calculate GCF of 13,53,920
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 13
:1,13
Now, list down the factors of 53
:1,53
Now, list down the factors of 920
:1,2,4,5,8,10,20,23,40,46,92,115,184,230,460,920
Greatest Common Factor
We found the factors 13,53,920 . The biggest common factor number is the GCF number.
So the greatest common factor 13,53,920 is 1.
Lets's calculate LCM of 218,103,309
103 | 218, 103, 309 |
218, 1, 3 |
∴ So the LCM of the given numbers is 103 x 218 x 1 x 3 = 67362
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/67362
Therefore, the GCF of Fractions 13/218,53/103,920/309 is 1/67362
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 218,103,309 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(218,103,309) = 1
common factors(in case of two or more numbers have common factors) = 103
GCF(218,103,309) x common factors =1 x 103 = 103
LCM(218,103,309) = ( 218 × 103 × 309 ) / 103
LCM(218,103,309) = 6938286 / 103
LCM(218,103,309) = 67362
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 13,53,920?
The HCF of 13,53,920 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 13/218, 53/103, 920/309?
Answer: GCF of Numerators as per given numbers 13/218, 53/103, 920/309 is
GCF of Numerators i.e. for 13,53,920 is 1
LCM of denominators i.e. for 218,103,309 is 67362.
Thus, GCF of Fractions is 1/67362.Finally, GCF of Fractions for 13/218, 53/103, 920/309 is 1/67362.