Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 50/99,14/30,820/165
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 50,14,820
Greatest Common Factor of Numerators i.e. GCF of 50,14,820 is 2 .
LCM of Denominators means LCM of 99,30,165 as per the given fractions.
LCM of 99,30,165 is 990 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 50,14,820
2 | 50, 14, 820 |
25, 7, 410 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 50
List of positive integer factors of 50 that divides 50 without a remainder.
1,2,5,10,25,50
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 820
List of positive integer factors of 820 that divides 820 without a remainder.
1,2,4,5,10,20,41,82,164,205,410,820
Greatest Common Factor
We found the factors 50,14,820 . The biggest common factor number is the GCF number.
So the greatest common factor 50,14,820 is 2.
Lets's calculate LCM of 99,30,165
3 | 99, 30, 165 |
5 | 33, 10, 55 |
11 | 33, 2, 11 |
3, 2, 1 |
∴ So the LCM of the given numbers is 3 x 5 x 11 x 3 x 2 x 1 = 990
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/990
Therefore, the GCF of Fractions 50/99,14/30,820/165 is 2/990
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 99,30,165 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(99,30,165) = 3
common factors(in case of two or more numbers have common factors) = 165
GCF(99,30,165) x common factors =3 x 165 = 495
LCM(99,30,165) = ( 99 × 30 × 165 ) / 495
LCM(99,30,165) = 490050 / 495
LCM(99,30,165) = 990
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 50/99, 14/30, 820/165?
Answer: GCF of Numerators as per given numbers 50/99, 14/30, 820/165 is
GCF of Numerators i.e. for 50,14,820 is 2
LCM of denominators i.e. for 99,30,165 is 990.
Thus, GCF of Fractions is 2/990.Finally, GCF of Fractions for 50/99, 14/30, 820/165 is 2/990.