Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 85/38,10/50,36/33,596/75
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 85,10,36,596
Greatest Common Factor of Numerators i.e. GCF of 85,10,36,596 is 1 .
LCM of Denominators means LCM of 38,50,33,75 as per the given fractions.
LCM of 38,50,33,75 is 31350 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 85,10,36,596
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 85
List of positive integer factors of 85 that divides 85 without a remainder.
1,5,17,85
Factors of 10
List of positive integer factors of 10 that divides 10 without a remainder.
1,2,5,10
Factors of 36
List of positive integer factors of 36 that divides 36 without a remainder.
1,2,3,4,6,9,12,18,36
Factors of 596
List of positive integer factors of 596 that divides 596 without a remainder.
1,2,4,149,298,596
Greatest Common Factor
We found the factors 85,10,36,596 . The biggest common factor number is the GCF number.
So the greatest common factor 85,10,36,596 is 1.
Lets's calculate LCM of 38,50,33,75
2 | 38, 50, 33, 75 |
3 | 19, 25, 33, 75 |
5 | 19, 25, 11, 25 |
5 | 19, 5, 11, 5 |
19, 1, 11, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 5 x 19 x 1 x 11 x 1 = 31350
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/31350
Therefore, the GCF of Fractions 85/38,10/50,36/33,596/75 is 1/31350
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 38,50,33,75 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(38,50,33,75) = 1
common factors(in case of two or more numbers have common factors) = 150
GCF(38,50,33,75) x common factors =1 x 150 = 150
LCM(38,50,33,75) = ( 38 × 50 × 33 × 75 ) / 150
LCM(38,50,33,75) = 4702500 / 150
LCM(38,50,33,75) = 31350
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 85/38, 10/50, 36/33, 596/75?
Answer: GCF of Numerators as per given numbers 85/38, 10/50, 36/33, 596/75 is
GCF of Numerators i.e. for 85,10,36,596 is 1
LCM of denominators i.e. for 38,50,33,75 is 31350.
Thus, GCF of Fractions is 1/31350.Finally, GCF of Fractions for 85/38, 10/50, 36/33, 596/75 is 1/31350.