Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 509/24,243/12,870/240
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 509,243,870
Greatest Common Factor of Numerators i.e. GCF of 509,243,870 is 1 .
LCM of Denominators means LCM of 24,12,240 as per the given fractions.
LCM of 24,12,240 is 240 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 509,243,870
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 509
List of positive integer factors of 509 that divides 509 without a remainder.
1,509
Factors of 243
List of positive integer factors of 243 that divides 243 without a remainder.
1,3,9,27,81,243
Factors of 870
List of positive integer factors of 870 that divides 870 without a remainder.
1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870
Greatest Common Factor
We found the factors 509,243,870 . The biggest common factor number is the GCF number.
So the greatest common factor 509,243,870 is 1.
Lets's calculate LCM of 24,12,240
2 | 24, 12, 240 |
2 | 12, 6, 120 |
2 | 3, 6, 60 |
3 | 3, 3, 30 |
1, 1, 10 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 1 x 1 x 10 = 240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/240
Therefore, the GCF of Fractions 509/24,243/12,870/240 is 1/240
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 24,12,240 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(24,12,240) = 12
common factors(in case of two or more numbers have common factors) = 24
GCF(24,12,240) x common factors =12 x 24 = 288
LCM(24,12,240) = ( 24 × 12 × 240 ) / 288
LCM(24,12,240) = 69120 / 288
LCM(24,12,240) = 240
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 509/24, 243/12, 870/240?
Answer: GCF of Numerators as per given numbers 509/24, 243/12, 870/240 is
GCF of Numerators i.e. for 509,243,870 is 1
LCM of denominators i.e. for 24,12,240 is 240.
Thus, GCF of Fractions is 1/240.Finally, GCF of Fractions for 509/24, 243/12, 870/240 is 1/240.