Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 342/77,285/91,133/754
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 342,285,133
Greatest Common Factor of Numerators i.e. GCF of 342,285,133 is 19 .
LCM of Denominators means LCM of 77,91,754 as per the given fractions.
LCM of 77,91,754 is 58058 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 342,285,133
19 | 342, 285, 133 |
18, 15, 7 |
∴ So the GCF of the given numbers is 19 = 19
Factors of 342
List of positive integer factors of 342 that divides 342 without a remainder.
1,2,3,6,9,18,19,38,57,114,171,342
Factors of 285
List of positive integer factors of 285 that divides 285 without a remainder.
1,3,5,15,19,57,95,285
Factors of 133
List of positive integer factors of 133 that divides 133 without a remainder.
1,7,19,133
Greatest Common Factor
We found the factors 342,285,133 . The biggest common factor number is the GCF number.
So the greatest common factor 342,285,133 is 19.
Lets's calculate LCM of 77,91,754
7 | 77, 91, 754 |
13 | 11, 13, 754 |
11, 1, 58 |
∴ So the LCM of the given numbers is 7 x 13 x 11 x 1 x 58 = 58058
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/58058
Therefore, the GCF of Fractions 342/77,285/91,133/754 is 19/58058
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 77,91,754 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,91,754) = 1
common factors(in case of two or more numbers have common factors) = 91
GCF(77,91,754) x common factors =1 x 91 = 91
LCM(77,91,754) = ( 77 × 91 × 754 ) / 91
LCM(77,91,754) = 5283278 / 91
LCM(77,91,754) = 58058
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 342/77, 285/91, 133/754?
Answer: GCF of Numerators as per given numbers 342/77, 285/91, 133/754 is
GCF of Numerators i.e. for 342,285,133 is 19
LCM of denominators i.e. for 77,91,754 is 58058.
Thus, GCF of Fractions is 19/58058.Finally, GCF of Fractions for 342/77, 285/91, 133/754 is 19/58058.