Use our free GCF of Fractions Calculator tool to compute the GCF of 115/218, 385/222 i.e 5/24198 easily. The following is the detailed procedure to determine the greatest common factor of fractions 115/218, 385/222.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 115/218,385/222
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 115/218,385/222, numerators are 115,385
Denominators are 218,222
The GCF of 115,385 is 5 .
LCM of 218,222 is 24198.
The greatest common factor of 115/218,385/222 = [GCF of 115,385]/[LCM of 218,222]= 5/24198
Therefore, the GCF of 115/218,385/222 is 5/24198.
To find the highest common factor of 115,385, we have to find the factors of both numbers and list the highest common factor.
The factors of 115 are 1, 5, 23, 115
The factors of 385 are 1, 5, 7, 11, 35, 55, 77, 385
The HCF of 115,385 is 5.
Lets's calculate GCF of 115,385
5 | 115, 385 |
23, 77 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 115
:1,5,23,115
Now, list down the factors of 385
:1,5,7,11,35,55,77,385
Greatest Common Factor
We found the factors 115,385 . The biggest common factor number is the GCF number.
So the greatest common factor 115,385 is 5.
Lets's calculate LCM of 218,222
2 | 218, 222 |
109, 111 |
∴ So the LCM of the given numbers is 2 x 109 x 111 = 24198
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/24198
Therefore, the GCF of Fractions 115/218,385/222 is 5/24198
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 218,222 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(218,222) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(218,222) x common factors =2 x 1 = 2
LCM(218,222) = ( 218 × 222 ) / 2
LCM(218,222) = 48396 / 2
LCM(218,222) = 24198
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 115,385?
The HCF of 115,385 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 115/218, 385/222?
Answer: GCF of Numerators as per given numbers 115/218, 385/222 is
GCF of Numerators i.e. for 115,385 is 5
LCM of denominators i.e. for 218,222 is 24198.
Thus, GCF of Fractions is 5/24198.Finally, GCF of Fractions for 115/218, 385/222 is 5/24198.