Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 40/12,64/85,81/60,71/53
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 40,64,81,71
Greatest Common Factor of Numerators i.e. GCF of 40,64,81,71 is 1 .
LCM of Denominators means LCM of 12,85,60,53 as per the given fractions.
LCM of 12,85,60,53 is 54060 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 40,64,81,71
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Factors of 64
List of positive integer factors of 64 that divides 64 without a remainder.
1,2,4,8,16,32,64
Factors of 81
List of positive integer factors of 81 that divides 81 without a remainder.
1,3,9,27,81
Factors of 71
List of positive integer factors of 71 that divides 71 without a remainder.
1,71
Greatest Common Factor
We found the factors 40,64,81,71 . The biggest common factor number is the GCF number.
So the greatest common factor 40,64,81,71 is 1.
Lets's calculate LCM of 12,85,60,53
2 | 12, 85, 60, 53 |
2 | 6, 85, 30, 53 |
3 | 3, 85, 15, 53 |
5 | 1, 85, 5, 53 |
1, 17, 1, 53 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 17 x 1 x 53 = 54060
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/54060
Therefore, the GCF of Fractions 40/12,64/85,81/60,71/53 is 1/54060
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 12,85,60,53 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,85,60,53) = 1
common factors(in case of two or more numbers have common factors) = 60
GCF(12,85,60,53) x common factors =1 x 60 = 60
LCM(12,85,60,53) = ( 12 × 85 × 60 × 53 ) / 60
LCM(12,85,60,53) = 3243600 / 60
LCM(12,85,60,53) = 54060
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 40/12, 64/85, 81/60, 71/53?
Answer: GCF of Numerators as per given numbers 40/12, 64/85, 81/60, 71/53 is
GCF of Numerators i.e. for 40,64,81,71 is 1
LCM of denominators i.e. for 12,85,60,53 is 54060.
Thus, GCF of Fractions is 1/54060.Finally, GCF of Fractions for 40/12, 64/85, 81/60, 71/53 is 1/54060.