Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 114/365,120/578
Formula to find GCF of Fractions is
GCF = GCF of Numerators/LCM of Denominators
As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators
In the given fractions GCF of Numerators means GCF of 114,120
Greatest Common Factor of Numerators i.e. GCF of 114,120 is 6 .
LCM of Denominators means LCM of 365,578 as per the given fractions.
LCM of 365,578 is 210970 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 114,120
2 | 114, 120 |
3 | 57, 60 |
19, 20 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Factors of 114
List of positive integer factors of 114 that divides 114 without a remainder.
1,2,3,6,19,38,57,114
Factors of 120
List of positive integer factors of 120 that divides 120 without a remainder.
1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 114,120 . The biggest common factor number is the GCF number.
So the greatest common factor 114,120 is 6.
Lets's calculate LCM of 365,578
Given numbers has no common factors except 1. So, there LCM is their product i.e 210970
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/210970
Therefore, the GCF of Fractions 114/365,120/578 is 6/210970
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 365,578 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(365,578) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(365,578) x common factors =1 x 1 = 1
LCM(365,578) = ( 365 × 578 ) / 1
LCM(365,578) = 210970 / 1
LCM(365,578) = 210970
Here are some samples of GCF of Fractions calculations.
Here are some samples of GCF of Fractions calculations.
1. 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.
2. What is the GCF of Fractions for 114/365, 120/578?
Answer: GCF of Numerators as per given numbers 114/365, 120/578 is
GCF of Numerators i.e. for 114,120 is 6
LCM of denominators i.e. for 365,578 is 210970.
Thus, GCF of Fractions is 6/210970.Finally, GCF of Fractions for 114/365, 120/578 is 6/210970.