Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 54/50,30/47,90/16,65/80
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 54,30,90,65
Greatest Common Factor of Numerators i.e. GCF of 54,30,90,65 is 1 .
LCM of Denominators means LCM of 50,47,16,80 as per the given fractions.
LCM of 50,47,16,80 is 18800 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 54,30,90,65
∴ So GCF of numbers is 1 because of no common factors present between them.
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 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Factors of 90
List of positive integer factors of 90 that divides 90 without a remainder.
1,2,3,5,6,9,10,15,18,30,45,90
Factors of 65
List of positive integer factors of 65 that divides 65 without a remainder.
1,5,13,65
Greatest Common Factor
We found the factors 54,30,90,65 . The biggest common factor number is the GCF number.
So the greatest common factor 54,30,90,65 is 1.
Lets's calculate LCM of 50,47,16,80
2 | 50, 47, 16, 80 |
2 | 25, 47, 8, 40 |
2 | 25, 47, 4, 20 |
2 | 25, 47, 2, 10 |
5 | 25, 47, 1, 5 |
1, 47, 1, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 5 x 1 x 47 x 1 x 5 = 18800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18800
Therefore, the GCF of Fractions 54/50,30/47,90/16,65/80 is 1/18800
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 50,47,16,80 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(50,47,16,80) = 1
common factors(in case of two or more numbers have common factors) = 160
GCF(50,47,16,80) x common factors =1 x 160 = 160
LCM(50,47,16,80) = ( 50 × 47 × 16 × 80 ) / 160
LCM(50,47,16,80) = 3008000 / 160
LCM(50,47,16,80) = 18800
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 54/50, 30/47, 90/16, 65/80?
Answer: GCF of Numerators as per given numbers 54/50, 30/47, 90/16, 65/80 is
GCF of Numerators i.e. for 54,30,90,65 is 1
LCM of denominators i.e. for 50,47,16,80 is 18800.
Thus, GCF of Fractions is 1/18800.Finally, GCF of Fractions for 54/50, 30/47, 90/16, 65/80 is 1/18800.