Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 66/40,36/75,57/30,45/970
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 66,36,57,45
Greatest Common Factor of Numerators i.e. GCF of 66,36,57,45 is 3 .
LCM of Denominators means LCM of 40,75,30,970 as per the given fractions.
LCM of 40,75,30,970 is 58200 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 66,36,57,45
3 | 66, 36, 57, 45 |
22, 12, 19, 15 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 66
List of positive integer factors of 66 that divides 66 without a remainder.
1,2,3,6,11,22,33,66
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 45
List of positive integer factors of 45 that divides 45 without a remainder.
1,3,5,9,15,45
Greatest Common Factor
We found the factors 66,36,57,45 . The biggest common factor number is the GCF number.
So the greatest common factor 66,36,57,45 is 3.
Lets's calculate LCM of 40,75,30,970
2 | 40, 75, 30, 970 |
3 | 20, 75, 15, 485 |
5 | 20, 25, 5, 485 |
4, 1, 5, 97 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 4 x 1 x 5 x 97 = 58200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/58200
Therefore, the GCF of Fractions 66/40,36/75,57/30,45/970 is 3/58200
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 40,75,30,970 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,75,30,970) = 5
common factors(in case of two or more numbers have common factors) = 300
GCF(40,75,30,970) x common factors =5 x 300 = 1500
LCM(40,75,30,970) = ( 40 × 75 × 30 × 970 ) / 1500
LCM(40,75,30,970) = 87300000 / 1500
LCM(40,75,30,970) = 58200
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 66/40, 36/75, 57/30, 45/970?
Answer: GCF of Numerators as per given numbers 66/40, 36/75, 57/30, 45/970 is
GCF of Numerators i.e. for 66,36,57,45 is 3
LCM of denominators i.e. for 40,75,30,970 is 58200.
Thus, GCF of Fractions is 3/58200.Finally, GCF of Fractions for 66/40, 36/75, 57/30, 45/970 is 3/58200.