Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 406/312,6034/215
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 406,6034
Greatest Common Factor of Numerators i.e. GCF of 406,6034 is 14 .
LCM of Denominators means LCM of 312,215 as per the given fractions.
LCM of 312,215 is 67080 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 406,6034
2 | 406, 6034 |
7 | 203, 3017 |
29, 431 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Factors of 406
List of positive integer factors of 406 that divides 406 without a remainder.
1,2,7,14,29,58,203,406
Factors of 6034
List of positive integer factors of 6034 that divides 6034 without a remainder.
1,2,7,14,431,862,3017,6034
Greatest Common Factor
We found the factors 406,6034 . The biggest common factor number is the GCF number.
So the greatest common factor 406,6034 is 14.
Lets's calculate LCM of 312,215
Given numbers has no common factors except 1. So, there LCM is their product i.e 67080
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/67080
Therefore, the GCF of Fractions 406/312,6034/215 is 14/67080
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 312,215 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,215) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(312,215) x common factors =1 x 1 = 1
LCM(312,215) = ( 312 × 215 ) / 1
LCM(312,215) = 67080 / 1
LCM(312,215) = 67080
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 406/312, 6034/215?
Answer: GCF of Numerators as per given numbers 406/312, 6034/215 is
GCF of Numerators i.e. for 406,6034 is 14
LCM of denominators i.e. for 312,215 is 67080.
Thus, GCF of Fractions is 14/67080.Finally, GCF of Fractions for 406/312, 6034/215 is 14/67080.