Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 198/56,620/64,405/72
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 198,620,405
Greatest Common Factor of Numerators i.e. GCF of 198,620,405 is 1 .
LCM of Denominators means LCM of 56,64,72 as per the given fractions.
LCM of 56,64,72 is 4032 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 198,620,405
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 198
List of positive integer factors of 198 that divides 198 without a remainder.
1,2,3,6,9,11,18,22,33,66,99,198
Factors of 620
List of positive integer factors of 620 that divides 620 without a remainder.
1,2,4,5,10,20,31,62,124,155,310,620
Factors of 405
List of positive integer factors of 405 that divides 405 without a remainder.
1,3,5,9,15,27,45,81,135,405
Greatest Common Factor
We found the factors 198,620,405 . The biggest common factor number is the GCF number.
So the greatest common factor 198,620,405 is 1.
Lets's calculate LCM of 56,64,72
2 | 56, 64, 72 |
2 | 28, 32, 36 |
2 | 14, 16, 18 |
7, 8, 9 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 7 x 8 x 9 = 4032
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4032
Therefore, the GCF of Fractions 198/56,620/64,405/72 is 1/4032
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 56,64,72 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(56,64,72) = 8
common factors(in case of two or more numbers have common factors) = 8
GCF(56,64,72) x common factors =8 x 8 = 64
LCM(56,64,72) = ( 56 × 64 × 72 ) / 64
LCM(56,64,72) = 258048 / 64
LCM(56,64,72) = 4032
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 198/56, 620/64, 405/72?
Answer: GCF of Numerators as per given numbers 198/56, 620/64, 405/72 is
GCF of Numerators i.e. for 198,620,405 is 1
LCM of denominators i.e. for 56,64,72 is 4032.
Thus, GCF of Fractions is 1/4032.Finally, GCF of Fractions for 198/56, 620/64, 405/72 is 1/4032.