Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 22/36,54/80,213/24
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 22,54,213
Greatest Common Factor of Numerators i.e. GCF of 22,54,213 is 1 .
LCM of Denominators means LCM of 36,80,24 as per the given fractions.
LCM of 36,80,24 is 720 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 22,54,213
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 22
List of positive integer factors of 22 that divides 22 without a remainder.
1,2,11,22
Factors of 54
List of positive integer factors of 54 that divides 54 without a remainder.
1,2,3,6,9,18,27,54
Factors of 213
List of positive integer factors of 213 that divides 213 without a remainder.
1,3,71,213
Greatest Common Factor
We found the factors 22,54,213 . The biggest common factor number is the GCF number.
So the greatest common factor 22,54,213 is 1.
Lets's calculate LCM of 36,80,24
2 | 36, 80, 24 |
2 | 18, 40, 12 |
2 | 9, 20, 6 |
3 | 9, 10, 3 |
1, 10, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 1 x 10 x 3 = 720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/720
Therefore, the GCF of Fractions 22/36,54/80,213/24 is 1/720
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 36,80,24 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(36,80,24) = 4
common factors(in case of two or more numbers have common factors) = 24
GCF(36,80,24) x common factors =4 x 24 = 96
LCM(36,80,24) = ( 36 × 80 × 24 ) / 96
LCM(36,80,24) = 69120 / 96
LCM(36,80,24) = 720
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 22/36, 54/80, 213/24?
Answer: GCF of Numerators as per given numbers 22/36, 54/80, 213/24 is
GCF of Numerators i.e. for 22,54,213 is 1
LCM of denominators i.e. for 36,80,24 is 720.
Thus, GCF of Fractions is 1/720.Finally, GCF of Fractions for 22/36, 54/80, 213/24 is 1/720.