Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 381/85,819/10,423/314
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 381,819,423
Greatest Common Factor of Numerators i.e. GCF of 381,819,423 is 3 .
LCM of Denominators means LCM of 85,10,314 as per the given fractions.
LCM of 85,10,314 is 26690 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 381,819,423
3 | 381, 819, 423 |
127, 273, 141 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 381
List of positive integer factors of 381 that divides 381 without a remainder.
1,3,127,381
Factors of 819
List of positive integer factors of 819 that divides 819 without a remainder.
1,3,7,9,13,21,39,63,91,117,273,819
Factors of 423
List of positive integer factors of 423 that divides 423 without a remainder.
1,3,9,47,141,423
Greatest Common Factor
We found the factors 381,819,423 . The biggest common factor number is the GCF number.
So the greatest common factor 381,819,423 is 3.
Lets's calculate LCM of 85,10,314
2 | 85, 10, 314 |
5 | 85, 5, 157 |
17, 1, 157 |
∴ So the LCM of the given numbers is 2 x 5 x 17 x 1 x 157 = 26690
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/26690
Therefore, the GCF of Fractions 381/85,819/10,423/314 is 3/26690
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 85,10,314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,10,314) = 1
common factors(in case of two or more numbers have common factors) = 10
GCF(85,10,314) x common factors =1 x 10 = 10
LCM(85,10,314) = ( 85 × 10 × 314 ) / 10
LCM(85,10,314) = 266900 / 10
LCM(85,10,314) = 26690
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 381/85, 819/10, 423/314?
Answer: GCF of Numerators as per given numbers 381/85, 819/10, 423/314 is
GCF of Numerators i.e. for 381,819,423 is 3
LCM of denominators i.e. for 85,10,314 is 26690.
Thus, GCF of Fractions is 3/26690.Finally, GCF of Fractions for 381/85, 819/10, 423/314 is 3/26690.