Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 60/48,10/43,54/16,202/14
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 60,10,54,202
Greatest Common Factor of Numerators i.e. GCF of 60,10,54,202 is 2 .
LCM of Denominators means LCM of 48,43,16,14 as per the given fractions.
LCM of 48,43,16,14 is 14448 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 60,10,54,202
2 | 60, 10, 54, 202 |
30, 5, 27, 101 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 60
List of positive integer factors of 60 that divides 60 without a remainder.
1,2,3,4,5,6,10,12,15,20,30,60
Factors of 10
List of positive integer factors of 10 that divides 10 without a remainder.
1,2,5,10
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 202
List of positive integer factors of 202 that divides 202 without a remainder.
1,2,101,202
Greatest Common Factor
We found the factors 60,10,54,202 . The biggest common factor number is the GCF number.
So the greatest common factor 60,10,54,202 is 2.
Lets's calculate LCM of 48,43,16,14
2 | 48, 43, 16, 14 |
2 | 24, 43, 8, 7 |
2 | 12, 43, 4, 7 |
2 | 6, 43, 2, 7 |
3, 43, 1, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 43 x 1 x 7 = 14448
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/14448
Therefore, the GCF of Fractions 60/48,10/43,54/16,202/14 is 2/14448
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 48,43,16,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(48,43,16,14) = 1
common factors(in case of two or more numbers have common factors) = 32
GCF(48,43,16,14) x common factors =1 x 32 = 32
LCM(48,43,16,14) = ( 48 × 43 × 16 × 14 ) / 32
LCM(48,43,16,14) = 462336 / 32
LCM(48,43,16,14) = 14448
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 60/48, 10/43, 54/16, 202/14?
Answer: GCF of Numerators as per given numbers 60/48, 10/43, 54/16, 202/14 is
GCF of Numerators i.e. for 60,10,54,202 is 2
LCM of denominators i.e. for 48,43,16,14 is 14448.
Thus, GCF of Fractions is 2/14448.Finally, GCF of Fractions for 60/48, 10/43, 54/16, 202/14 is 2/14448.