Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 99/86,40/17,14/12,72/204
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 99,40,14,72
Greatest Common Factor of Numerators i.e. GCF of 99,40,14,72 is 1 .
LCM of Denominators means LCM of 86,17,12,204 as per the given fractions.
LCM of 86,17,12,204 is 8772 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 99,40,14,72
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 99
List of positive integer factors of 99 that divides 99 without a remainder.
1,3,9,11,33,99
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 72
List of positive integer factors of 72 that divides 72 without a remainder.
1,2,3,4,6,8,9,12,18,24,36,72
Greatest Common Factor
We found the factors 99,40,14,72 . The biggest common factor number is the GCF number.
So the greatest common factor 99,40,14,72 is 1.
Lets's calculate LCM of 86,17,12,204
2 | 86, 17, 12, 204 |
2 | 43, 17, 6, 102 |
3 | 43, 17, 3, 51 |
17 | 43, 17, 1, 17 |
43, 1, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 17 x 43 x 1 x 1 x 1 = 8772
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8772
Therefore, the GCF of Fractions 99/86,40/17,14/12,72/204 is 1/8772
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 86,17,12,204 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(86,17,12,204) = 1
common factors(in case of two or more numbers have common factors) = 408
GCF(86,17,12,204) x common factors =1 x 408 = 408
LCM(86,17,12,204) = ( 86 × 17 × 12 × 204 ) / 408
LCM(86,17,12,204) = 3578976 / 408
LCM(86,17,12,204) = 8772
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 99/86, 40/17, 14/12, 72/204?
Answer: GCF of Numerators as per given numbers 99/86, 40/17, 14/12, 72/204 is
GCF of Numerators i.e. for 99,40,14,72 is 1
LCM of denominators i.e. for 86,17,12,204 is 8772.
Thus, GCF of Fractions is 1/8772.Finally, GCF of Fractions for 99/86, 40/17, 14/12, 72/204 is 1/8772.