Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 70/10,96/102,309/310
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 70,96,309
Greatest Common Factor of Numerators i.e. GCF of 70,96,309 is 1 .
LCM of Denominators means LCM of 10,102,310 as per the given fractions.
LCM of 10,102,310 is 15810 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 70,96,309
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 70
List of positive integer factors of 70 that divides 70 without a remainder.
1,2,5,7,10,14,35,70
Factors of 96
List of positive integer factors of 96 that divides 96 without a remainder.
1,2,3,4,6,8,12,16,24,32,48,96
Factors of 309
List of positive integer factors of 309 that divides 309 without a remainder.
1,3,103,309
Greatest Common Factor
We found the factors 70,96,309 . The biggest common factor number is the GCF number.
So the greatest common factor 70,96,309 is 1.
Lets's calculate LCM of 10,102,310
2 | 10, 102, 310 |
5 | 5, 51, 155 |
1, 51, 31 |
∴ So the LCM of the given numbers is 2 x 5 x 1 x 51 x 31 = 15810
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15810
Therefore, the GCF of Fractions 70/10,96/102,309/310 is 1/15810
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 10,102,310 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(10,102,310) = 2
common factors(in case of two or more numbers have common factors) = 10
GCF(10,102,310) x common factors =2 x 10 = 20
LCM(10,102,310) = ( 10 × 102 × 310 ) / 20
LCM(10,102,310) = 316200 / 20
LCM(10,102,310) = 15810
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 70/10, 96/102, 309/310?
Answer: GCF of Numerators as per given numbers 70/10, 96/102, 309/310 is
GCF of Numerators i.e. for 70,96,309 is 1
LCM of denominators i.e. for 10,102,310 is 15810.
Thus, GCF of Fractions is 1/15810.Finally, GCF of Fractions for 70/10, 96/102, 309/310 is 1/15810.