Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 76/41,54/90,214/31
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 76,54,214
Greatest Common Factor of Numerators i.e. GCF of 76,54,214 is 2 .
LCM of Denominators means LCM of 41,90,31 as per the given fractions.
LCM of 41,90,31 is 114390 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 76,54,214
2 | 76, 54, 214 |
38, 27, 107 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 76
List of positive integer factors of 76 that divides 76 without a remainder.
1,2,4,19,38,76
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 214
List of positive integer factors of 214 that divides 214 without a remainder.
1,2,107,214
Greatest Common Factor
We found the factors 76,54,214 . The biggest common factor number is the GCF number.
So the greatest common factor 76,54,214 is 2.
Lets's calculate LCM of 41,90,31
Given numbers has no common factors except 1. So, there LCM is their product i.e 114390
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/114390
Therefore, the GCF of Fractions 76/41,54/90,214/31 is 2/114390
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 41,90,31 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(41,90,31) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(41,90,31) x common factors =1 x 1 = 1
LCM(41,90,31) = ( 41 × 90 × 31 ) / 1
LCM(41,90,31) = 114390 / 1
LCM(41,90,31) = 114390
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 76/41, 54/90, 214/31?
Answer: GCF of Numerators as per given numbers 76/41, 54/90, 214/31 is
GCF of Numerators i.e. for 76,54,214 is 2
LCM of denominators i.e. for 41,90,31 is 114390.
Thus, GCF of Fractions is 2/114390.Finally, GCF of Fractions for 76/41, 54/90, 214/31 is 2/114390.