Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 68/54,65/31,561/226
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 68,65,561
Greatest Common Factor of Numerators i.e. GCF of 68,65,561 is 1 .
LCM of Denominators means LCM of 54,31,226 as per the given fractions.
LCM of 54,31,226 is 189162 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 68,65,561
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1,2,4,17,34,68
Factors of 65
List of positive integer factors of 65 that divides 65 without a remainder.
1,5,13,65
Factors of 561
List of positive integer factors of 561 that divides 561 without a remainder.
1,3,11,17,33,51,187,561
Greatest Common Factor
We found the factors 68,65,561 . The biggest common factor number is the GCF number.
So the greatest common factor 68,65,561 is 1.
Lets's calculate LCM of 54,31,226
2 | 54, 31, 226 |
27, 31, 113 |
∴ So the LCM of the given numbers is 2 x 27 x 31 x 113 = 189162
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/189162
Therefore, the GCF of Fractions 68/54,65/31,561/226 is 1/189162
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 54,31,226 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,31,226) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(54,31,226) x common factors =1 x 2 = 2
LCM(54,31,226) = ( 54 × 31 × 226 ) / 2
LCM(54,31,226) = 378324 / 2
LCM(54,31,226) = 189162
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 68/54, 65/31, 561/226?
Answer: GCF of Numerators as per given numbers 68/54, 65/31, 561/226 is
GCF of Numerators i.e. for 68,65,561 is 1
LCM of denominators i.e. for 54,31,226 is 189162.
Thus, GCF of Fractions is 1/189162.Finally, GCF of Fractions for 68/54, 65/31, 561/226 is 1/189162.