Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 105/75,741/5958
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 105,741
Greatest Common Factor of Numerators i.e. GCF of 105,741 is 3 .
LCM of Denominators means LCM of 75,5958 as per the given fractions.
LCM of 75,5958 is 148950 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 105,741
3 | 105, 741 |
35, 247 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 105
List of positive integer factors of 105 that divides 105 without a remainder.
1,3,5,7,15,21,35,105
Factors of 741
List of positive integer factors of 741 that divides 741 without a remainder.
1,3,13,19,39,57,247,741
Greatest Common Factor
We found the factors 105,741 . The biggest common factor number is the GCF number.
So the greatest common factor 105,741 is 3.
Lets's calculate LCM of 75,5958
3 | 75, 5958 |
25, 1986 |
∴ So the LCM of the given numbers is 3 x 25 x 1986 = 148950
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/148950
Therefore, the GCF of Fractions 105/75,741/5958 is 3/148950
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 75,5958 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,5958) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(75,5958) x common factors =3 x 1 = 3
LCM(75,5958) = ( 75 × 5958 ) / 3
LCM(75,5958) = 446850 / 3
LCM(75,5958) = 148950
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 105/75, 741/5958?
Answer: GCF of Numerators as per given numbers 105/75, 741/5958 is
GCF of Numerators i.e. for 105,741 is 3
LCM of denominators i.e. for 75,5958 is 148950.
Thus, GCF of Fractions is 3/148950.Finally, GCF of Fractions for 105/75, 741/5958 is 3/148950.