Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 32/16,87/23,60/77,14/966
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 32,87,60,14
Greatest Common Factor of Numerators i.e. GCF of 32,87,60,14 is 1 .
LCM of Denominators means LCM of 16,23,77,966 as per the given fractions.
LCM of 16,23,77,966 is 85008 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 32,87,60,14
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 32
List of positive integer factors of 32 that divides 32 without a remainder.
1,2,4,8,16,32
Factors of 87
List of positive integer factors of 87 that divides 87 without a remainder.
1,3,29,87
Factors of 60
List of positive integer factors of 60 that divides 60 without a remainder.
1,2,3,4,5,6,10,12,15,20,30,60
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Greatest Common Factor
We found the factors 32,87,60,14 . The biggest common factor number is the GCF number.
So the greatest common factor 32,87,60,14 is 1.
Lets's calculate LCM of 16,23,77,966
2 | 16, 23, 77, 966 |
7 | 8, 23, 77, 483 |
23 | 8, 23, 11, 69 |
8, 1, 11, 3 |
∴ So the LCM of the given numbers is 2 x 7 x 23 x 8 x 1 x 11 x 3 = 85008
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/85008
Therefore, the GCF of Fractions 32/16,87/23,60/77,14/966 is 1/85008
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 16,23,77,966 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,23,77,966) = 1
common factors(in case of two or more numbers have common factors) = 322
GCF(16,23,77,966) x common factors =1 x 322 = 322
LCM(16,23,77,966) = ( 16 × 23 × 77 × 966 ) / 322
LCM(16,23,77,966) = 27372576 / 322
LCM(16,23,77,966) = 85008
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 32/16, 87/23, 60/77, 14/966?
Answer: GCF of Numerators as per given numbers 32/16, 87/23, 60/77, 14/966 is
GCF of Numerators i.e. for 32,87,60,14 is 1
LCM of denominators i.e. for 16,23,77,966 is 85008.
Thus, GCF of Fractions is 1/85008.Finally, GCF of Fractions for 32/16, 87/23, 60/77, 14/966 is 1/85008.