Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 12/55,33/69,138/966
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 12,33,138
Greatest Common Factor of Numerators i.e. GCF of 12,33,138 is 3 .
LCM of Denominators means LCM of 55,69,966 as per the given fractions.
LCM of 55,69,966 is 53130 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 12,33,138
3 | 12, 33, 138 |
4, 11, 46 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1,2,3,4,6,12
Factors of 33
List of positive integer factors of 33 that divides 33 without a remainder.
1,3,11,33
Factors of 138
List of positive integer factors of 138 that divides 138 without a remainder.
1,2,3,6,23,46,69,138
Greatest Common Factor
We found the factors 12,33,138 . The biggest common factor number is the GCF number.
So the greatest common factor 12,33,138 is 3.
Lets's calculate LCM of 55,69,966
3 | 55, 69, 966 |
23 | 55, 23, 322 |
55, 1, 14 |
∴ So the LCM of the given numbers is 3 x 23 x 55 x 1 x 14 = 53130
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/53130
Therefore, the GCF of Fractions 12/55,33/69,138/966 is 3/53130
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 55,69,966 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(55,69,966) = 1
common factors(in case of two or more numbers have common factors) = 69
GCF(55,69,966) x common factors =1 x 69 = 69
LCM(55,69,966) = ( 55 × 69 × 966 ) / 69
LCM(55,69,966) = 3665970 / 69
LCM(55,69,966) = 53130
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 12/55, 33/69, 138/966?
Answer: GCF of Numerators as per given numbers 12/55, 33/69, 138/966 is
GCF of Numerators i.e. for 12,33,138 is 3
LCM of denominators i.e. for 55,69,966 is 53130.
Thus, GCF of Fractions is 3/53130.Finally, GCF of Fractions for 12/55, 33/69, 138/966 is 3/53130.