Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 35/13,65/27,45/63,54/268
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 35,65,45,54
Greatest Common Factor of Numerators i.e. GCF of 35,65,45,54 is 1 .
LCM of Denominators means LCM of 13,27,63,268 as per the given fractions.
LCM of 13,27,63,268 is 658476 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 35,65,45,54
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 35
List of positive integer factors of 35 that divides 35 without a remainder.
1,5,7,35
Factors of 65
List of positive integer factors of 65 that divides 65 without a remainder.
1,5,13,65
Factors of 45
List of positive integer factors of 45 that divides 45 without a remainder.
1,3,5,9,15,45
Factors of 54
List of positive integer factors of 54 that divides 54 without a remainder.
1,2,3,6,9,18,27,54
Greatest Common Factor
We found the factors 35,65,45,54 . The biggest common factor number is the GCF number.
So the greatest common factor 35,65,45,54 is 1.
Lets's calculate LCM of 13,27,63,268
3 | 13, 27, 63, 268 |
3 | 13, 9, 21, 268 |
13, 3, 7, 268 |
∴ So the LCM of the given numbers is 3 x 3 x 13 x 3 x 7 x 268 = 658476
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/658476
Therefore, the GCF of Fractions 35/13,65/27,45/63,54/268 is 1/658476
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 13,27,63,268 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(13,27,63,268) = 1
common factors(in case of two or more numbers have common factors) = 9
GCF(13,27,63,268) x common factors =1 x 9 = 9
LCM(13,27,63,268) = ( 13 × 27 × 63 × 268 ) / 9
LCM(13,27,63,268) = 5926284 / 9
LCM(13,27,63,268) = 658476
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 35/13, 65/27, 45/63, 54/268?
Answer: GCF of Numerators as per given numbers 35/13, 65/27, 45/63, 54/268 is
GCF of Numerators i.e. for 35,65,45,54 is 1
LCM of denominators i.e. for 13,27,63,268 is 658476.
Thus, GCF of Fractions is 1/658476.Finally, GCF of Fractions for 35/13, 65/27, 45/63, 54/268 is 1/658476.