Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 30/170,33/909,207/954
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 30,33,207
Greatest Common Factor of Numerators i.e. GCF of 30,33,207 is 3 .
LCM of Denominators means LCM of 170,909,954 as per the given fractions.
LCM of 170,909,954 is 8190090 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 30,33,207
3 | 30, 33, 207 |
10, 11, 69 |
∴ So the GCF of the given numbers is 3 = 3
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 33
List of positive integer factors of 33 that divides 33 without a remainder.
1,3,11,33
Factors of 207
List of positive integer factors of 207 that divides 207 without a remainder.
1,3,9,23,69,207
Greatest Common Factor
We found the factors 30,33,207 . The biggest common factor number is the GCF number.
So the greatest common factor 30,33,207 is 3.
Lets's calculate LCM of 170,909,954
2 | 170, 909, 954 |
3 | 85, 909, 477 |
3 | 85, 303, 159 |
85, 101, 53 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 85 x 101 x 53 = 8190090
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/8190090
Therefore, the GCF of Fractions 30/170,33/909,207/954 is 3/8190090
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 170,909,954 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(170,909,954) = 1
common factors(in case of two or more numbers have common factors) = 18
GCF(170,909,954) x common factors =1 x 18 = 18
LCM(170,909,954) = ( 170 × 909 × 954 ) / 18
LCM(170,909,954) = 147421620 / 18
LCM(170,909,954) = 8190090
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 30/170, 33/909, 207/954?
Answer: GCF of Numerators as per given numbers 30/170, 33/909, 207/954 is
GCF of Numerators i.e. for 30,33,207 is 3
LCM of denominators i.e. for 170,909,954 is 8190090.
Thus, GCF of Fractions is 3/8190090.Finally, GCF of Fractions for 30/170, 33/909, 207/954 is 3/8190090.