Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 3/20,1/42,83/35,54/243
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 3,1,83,54
Greatest Common Factor of Numerators i.e. GCF of 3,1,83,54 is 1 .
LCM of Denominators means LCM of 20,42,35,243 as per the given fractions.
LCM of 20,42,35,243 is 34020 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 3,1,83,54
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 3
List of positive integer factors of 3 that divides 3 without a remainder.
1,3
Factors of 1
List of positive integer factors of 1 that divides 1 without a remainder.
1
Factors of 83
List of positive integer factors of 83 that divides 83 without a remainder.
1,83
Factors of 54
List of positive integer factors of 54 that divides 54 without a remainder.
1,2,3,6,9,18,27,54
Greatest Common Factor
We found the factors 3,1,83,54 . The biggest common factor number is the GCF number.
So the greatest common factor 3,1,83,54 is 1.
Lets's calculate LCM of 20,42,35,243
2 | 20, 42, 35, 243 |
3 | 10, 21, 35, 243 |
5 | 10, 7, 35, 81 |
7 | 2, 7, 7, 81 |
2, 1, 1, 81 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 2 x 1 x 1 x 81 = 34020
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/34020
Therefore, the GCF of Fractions 3/20,1/42,83/35,54/243 is 1/34020
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 20,42,35,243 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,42,35,243) = 1
common factors(in case of two or more numbers have common factors) = 210
GCF(20,42,35,243) x common factors =1 x 210 = 210
LCM(20,42,35,243) = ( 20 × 42 × 35 × 243 ) / 210
LCM(20,42,35,243) = 7144200 / 210
LCM(20,42,35,243) = 34020
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 3/20, 1/42, 83/35, 54/243?
Answer: GCF of Numerators as per given numbers 3/20, 1/42, 83/35, 54/243 is
GCF of Numerators i.e. for 3,1,83,54 is 1
LCM of denominators i.e. for 20,42,35,243 is 34020.
Thus, GCF of Fractions is 1/34020.Finally, GCF of Fractions for 3/20, 1/42, 83/35, 54/243 is 1/34020.