Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 81/78,756/72,440/99
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 81,756,440
Greatest Common Factor of Numerators i.e. GCF of 81,756,440 is 1 .
LCM of Denominators means LCM of 78,72,99 as per the given fractions.
LCM of 78,72,99 is 10296 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 81,756,440
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 81
List of positive integer factors of 81 that divides 81 without a remainder.
1,3,9,27,81
Factors of 756
List of positive integer factors of 756 that divides 756 without a remainder.
1,2,3,4,6,7,9,12,14,18,21,27,28,36,42,54,63,84,108,126,189,252,378,756
Factors of 440
List of positive integer factors of 440 that divides 440 without a remainder.
1,2,4,5,8,10,11,20,22,40,44,55,88,110,220,440
Greatest Common Factor
We found the factors 81,756,440 . The biggest common factor number is the GCF number.
So the greatest common factor 81,756,440 is 1.
Lets's calculate LCM of 78,72,99
2 | 78, 72, 99 |
3 | 39, 36, 99 |
3 | 13, 12, 33 |
13, 4, 11 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 13 x 4 x 11 = 10296
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10296
Therefore, the GCF of Fractions 81/78,756/72,440/99 is 1/10296
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 78,72,99 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,72,99) = 3
common factors(in case of two or more numbers have common factors) = 18
GCF(78,72,99) x common factors =3 x 18 = 54
LCM(78,72,99) = ( 78 × 72 × 99 ) / 54
LCM(78,72,99) = 555984 / 54
LCM(78,72,99) = 10296
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 81/78, 756/72, 440/99?
Answer: GCF of Numerators as per given numbers 81/78, 756/72, 440/99 is
GCF of Numerators i.e. for 81,756,440 is 1
LCM of denominators i.e. for 78,72,99 is 10296.
Thus, GCF of Fractions is 1/10296.Finally, GCF of Fractions for 81/78, 756/72, 440/99 is 1/10296.