Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 75/39,34/99,41/90,76/33
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 75,34,41,76
Greatest Common Factor of Numerators i.e. GCF of 75,34,41,76 is 1 .
LCM of Denominators means LCM of 39,99,90,33 as per the given fractions.
LCM of 39,99,90,33 is 12870 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 75,34,41,76
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Factors of 34
List of positive integer factors of 34 that divides 34 without a remainder.
1,2,17,34
Factors of 41
List of positive integer factors of 41 that divides 41 without a remainder.
1,41
Factors of 76
List of positive integer factors of 76 that divides 76 without a remainder.
1,2,4,19,38,76
Greatest Common Factor
We found the factors 75,34,41,76 . The biggest common factor number is the GCF number.
So the greatest common factor 75,34,41,76 is 1.
Lets's calculate LCM of 39,99,90,33
3 | 39, 99, 90, 33 |
3 | 13, 33, 30, 11 |
11 | 13, 11, 10, 11 |
13, 1, 10, 1 |
∴ So the LCM of the given numbers is 3 x 3 x 11 x 13 x 1 x 10 x 1 = 12870
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12870
Therefore, the GCF of Fractions 75/39,34/99,41/90,76/33 is 1/12870
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 39,99,90,33 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(39,99,90,33) = 3
common factors(in case of two or more numbers have common factors) = 297
GCF(39,99,90,33) x common factors =3 x 297 = 891
LCM(39,99,90,33) = ( 39 × 99 × 90 × 33 ) / 891
LCM(39,99,90,33) = 11467170 / 891
LCM(39,99,90,33) = 12870
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 75/39, 34/99, 41/90, 76/33?
Answer: GCF of Numerators as per given numbers 75/39, 34/99, 41/90, 76/33 is
GCF of Numerators i.e. for 75,34,41,76 is 1
LCM of denominators i.e. for 39,99,90,33 is 12870.
Thus, GCF of Fractions is 1/12870.Finally, GCF of Fractions for 75/39, 34/99, 41/90, 76/33 is 1/12870.