Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 36/45,57/45,99/49,82/17
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 36,57,99,82
Greatest Common Factor of Numerators i.e. GCF of 36,57,99,82 is 1 .
LCM of Denominators means LCM of 45,45,49,17 as per the given fractions.
LCM of 45,45,49,17 is 37485 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 36,57,99,82
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 36
List of positive integer factors of 36 that divides 36 without a remainder.
1,2,3,4,6,9,12,18,36
Factors of 57
List of positive integer factors of 57 that divides 57 without a remainder.
1,3,19,57
Factors of 99
List of positive integer factors of 99 that divides 99 without a remainder.
1,3,9,11,33,99
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
Greatest Common Factor
We found the factors 36,57,99,82 . The biggest common factor number is the GCF number.
So the greatest common factor 36,57,99,82 is 1.
Lets's calculate LCM of 45,45,49,17
3 | 45, 45, 49, 17 |
3 | 15, 15, 49, 17 |
5 | 5, 5, 49, 17 |
1, 1, 49, 17 |
∴ So the LCM of the given numbers is 3 x 3 x 5 x 1 x 1 x 49 x 17 = 37485
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/37485
Therefore, the GCF of Fractions 36/45,57/45,99/49,82/17 is 1/37485
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 45,45,49,17 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(45,45,49,17) = 1
common factors(in case of two or more numbers have common factors) = 45
GCF(45,45,49,17) x common factors =1 x 45 = 45
LCM(45,45,49,17) = ( 45 × 45 × 49 × 17 ) / 45
LCM(45,45,49,17) = 1686825 / 45
LCM(45,45,49,17) = 37485
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 36/45, 57/45, 99/49, 82/17?
Answer: GCF of Numerators as per given numbers 36/45, 57/45, 99/49, 82/17 is
GCF of Numerators i.e. for 36,57,99,82 is 1
LCM of denominators i.e. for 45,45,49,17 is 37485.
Thus, GCF of Fractions is 1/37485.Finally, GCF of Fractions for 36/45, 57/45, 99/49, 82/17 is 1/37485.