Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 30/17,81/54,46/82,10/114
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 30,81,46,10
Greatest Common Factor of Numerators i.e. GCF of 30,81,46,10 is 1 .
LCM of Denominators means LCM of 17,54,82,114 as per the given fractions.
LCM of 17,54,82,114 is 715122 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 30,81,46,10
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Factors of 81
List of positive integer factors of 81 that divides 81 without a remainder.
1,3,9,27,81
Factors of 46
List of positive integer factors of 46 that divides 46 without a remainder.
1,2,23,46
Factors of 10
List of positive integer factors of 10 that divides 10 without a remainder.
1,2,5,10
Greatest Common Factor
We found the factors 30,81,46,10 . The biggest common factor number is the GCF number.
So the greatest common factor 30,81,46,10 is 1.
Lets's calculate LCM of 17,54,82,114
2 | 17, 54, 82, 114 |
3 | 17, 27, 41, 57 |
17, 9, 41, 19 |
∴ So the LCM of the given numbers is 2 x 3 x 17 x 9 x 41 x 19 = 715122
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/715122
Therefore, the GCF of Fractions 30/17,81/54,46/82,10/114 is 1/715122
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 17,54,82,114 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(17,54,82,114) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(17,54,82,114) x common factors =1 x 12 = 12
LCM(17,54,82,114) = ( 17 × 54 × 82 × 114 ) / 12
LCM(17,54,82,114) = 8581464 / 12
LCM(17,54,82,114) = 715122
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 30/17, 81/54, 46/82, 10/114?
Answer: GCF of Numerators as per given numbers 30/17, 81/54, 46/82, 10/114 is
GCF of Numerators i.e. for 30,81,46,10 is 1
LCM of denominators i.e. for 17,54,82,114 is 715122.
Thus, GCF of Fractions is 1/715122.Finally, GCF of Fractions for 30/17, 81/54, 46/82, 10/114 is 1/715122.