Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 9/30,753/75,411/21
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 9,753,411
Greatest Common Factor of Numerators i.e. GCF of 9,753,411 is 3 .
LCM of Denominators means LCM of 30,75,21 as per the given fractions.
LCM of 30,75,21 is 1050 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 9,753,411
3 | 9, 753, 411 |
3, 251, 137 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 9
List of positive integer factors of 9 that divides 9 without a remainder.
1,3,9
Factors of 753
List of positive integer factors of 753 that divides 753 without a remainder.
1,3,251,753
Factors of 411
List of positive integer factors of 411 that divides 411 without a remainder.
1,3,137,411
Greatest Common Factor
We found the factors 9,753,411 . The biggest common factor number is the GCF number.
So the greatest common factor 9,753,411 is 3.
Lets's calculate LCM of 30,75,21
3 | 30, 75, 21 |
5 | 10, 25, 7 |
2, 5, 7 |
∴ So the LCM of the given numbers is 3 x 5 x 2 x 5 x 7 = 1050
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1050
Therefore, the GCF of Fractions 9/30,753/75,411/21 is 3/1050
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 30,75,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,75,21) = 3
common factors(in case of two or more numbers have common factors) = 15
GCF(30,75,21) x common factors =3 x 15 = 45
LCM(30,75,21) = ( 30 × 75 × 21 ) / 45
LCM(30,75,21) = 47250 / 45
LCM(30,75,21) = 1050
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 9/30, 753/75, 411/21?
Answer: GCF of Numerators as per given numbers 9/30, 753/75, 411/21 is
GCF of Numerators i.e. for 9,753,411 is 3
LCM of denominators i.e. for 30,75,21 is 1050.
Thus, GCF of Fractions is 3/1050.Finally, GCF of Fractions for 9/30, 753/75, 411/21 is 3/1050.