Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 308/18,315/16,294/27
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 308,315,294
Greatest Common Factor of Numerators i.e. GCF of 308,315,294 is 7 .
LCM of Denominators means LCM of 18,16,27 as per the given fractions.
LCM of 18,16,27 is 432 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 308,315,294
7 | 308, 315, 294 |
44, 45, 42 |
∴ So the GCF of the given numbers is 7 = 7
Factors of 308
List of positive integer factors of 308 that divides 308 without a remainder.
1,2,4,7,11,14,22,28,44,77,154,308
Factors of 315
List of positive integer factors of 315 that divides 315 without a remainder.
1,3,5,7,9,15,21,35,45,63,105,315
Factors of 294
List of positive integer factors of 294 that divides 294 without a remainder.
1,2,3,6,7,14,21,42,49,98,147,294
Greatest Common Factor
We found the factors 308,315,294 . The biggest common factor number is the GCF number.
So the greatest common factor 308,315,294 is 7.
Lets's calculate LCM of 18,16,27
2 | 18, 16, 27 |
3 | 9, 8, 27 |
3 | 3, 8, 9 |
1, 8, 3 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 1 x 8 x 3 = 432
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/432
Therefore, the GCF of Fractions 308/18,315/16,294/27 is 7/432
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 18,16,27 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(18,16,27) = 1
common factors(in case of two or more numbers have common factors) = 18
GCF(18,16,27) x common factors =1 x 18 = 18
LCM(18,16,27) = ( 18 × 16 × 27 ) / 18
LCM(18,16,27) = 7776 / 18
LCM(18,16,27) = 432
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 308/18, 315/16, 294/27?
Answer: GCF of Numerators as per given numbers 308/18, 315/16, 294/27 is
GCF of Numerators i.e. for 308,315,294 is 7
LCM of denominators i.e. for 18,16,27 is 432.
Thus, GCF of Fractions is 7/432.Finally, GCF of Fractions for 308/18, 315/16, 294/27 is 7/432.