Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 19/73,90/84,109/180
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 19,90,109
Greatest Common Factor of Numerators i.e. GCF of 19,90,109 is 1 .
LCM of Denominators means LCM of 73,84,180 as per the given fractions.
LCM of 73,84,180 is 91980 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 19,90,109
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 19
List of positive integer factors of 19 that divides 19 without a remainder.
1,19
Factors of 90
List of positive integer factors of 90 that divides 90 without a remainder.
1,2,3,5,6,9,10,15,18,30,45,90
Factors of 109
List of positive integer factors of 109 that divides 109 without a remainder.
1,109
Greatest Common Factor
We found the factors 19,90,109 . The biggest common factor number is the GCF number.
So the greatest common factor 19,90,109 is 1.
Lets's calculate LCM of 73,84,180
2 | 73, 84, 180 |
2 | 73, 42, 90 |
3 | 73, 21, 45 |
73, 7, 15 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 73 x 7 x 15 = 91980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/91980
Therefore, the GCF of Fractions 19/73,90/84,109/180 is 1/91980
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 73,84,180 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(73,84,180) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(73,84,180) x common factors =1 x 12 = 12
LCM(73,84,180) = ( 73 × 84 × 180 ) / 12
LCM(73,84,180) = 1103760 / 12
LCM(73,84,180) = 91980
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 19/73, 90/84, 109/180?
Answer: GCF of Numerators as per given numbers 19/73, 90/84, 109/180 is
GCF of Numerators i.e. for 19,90,109 is 1
LCM of denominators i.e. for 73,84,180 is 91980.
Thus, GCF of Fractions is 1/91980.Finally, GCF of Fractions for 19/73, 90/84, 109/180 is 1/91980.