Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 39/675,75/177,378/207
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 39,75,378
Greatest Common Factor of Numerators i.e. GCF of 39,75,378 is 3 .
LCM of Denominators means LCM of 675,177,207 as per the given fractions.
LCM of 675,177,207 is 915975 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 39,75,378
3 | 39, 75, 378 |
13, 25, 126 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 39
List of positive integer factors of 39 that divides 39 without a remainder.
1,3,13,39
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Factors of 378
List of positive integer factors of 378 that divides 378 without a remainder.
1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Greatest Common Factor
We found the factors 39,75,378 . The biggest common factor number is the GCF number.
So the greatest common factor 39,75,378 is 3.
Lets's calculate LCM of 675,177,207
3 | 675, 177, 207 |
3 | 225, 59, 69 |
75, 59, 23 |
∴ So the LCM of the given numbers is 3 x 3 x 75 x 59 x 23 = 915975
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/915975
Therefore, the GCF of Fractions 39/675,75/177,378/207 is 3/915975
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 675,177,207 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(675,177,207) = 3
common factors(in case of two or more numbers have common factors) = 9
GCF(675,177,207) x common factors =3 x 9 = 27
LCM(675,177,207) = ( 675 × 177 × 207 ) / 27
LCM(675,177,207) = 24731325 / 27
LCM(675,177,207) = 915975
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 39/675, 75/177, 378/207?
Answer: GCF of Numerators as per given numbers 39/675, 75/177, 378/207 is
GCF of Numerators i.e. for 39,75,378 is 3
LCM of denominators i.e. for 675,177,207 is 915975.
Thus, GCF of Fractions is 3/915975.Finally, GCF of Fractions for 39/675, 75/177, 378/207 is 3/915975.