Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 216/645,8160/9890
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 216,8160
Greatest Common Factor of Numerators i.e. GCF of 216,8160 is 24 .
LCM of Denominators means LCM of 645,9890 as per the given fractions.
LCM of 645,9890 is 29670 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 216,8160
2 | 216, 8160 |
2 | 108, 4080 |
2 | 54, 2040 |
3 | 27, 1020 |
9, 340 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Factors of 216
List of positive integer factors of 216 that divides 216 without a remainder.
1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
Factors of 8160
List of positive integer factors of 8160 that divides 8160 without a remainder.
1,2,3,4,5,6,8,10,12,15,16,17,20,24,30,32,34,40,48,51,60,68,80,85,96,102,120,136,160,170,204,240,255,272,340,408,480,510,544,680,816,1020,1360,1632,2040,2720,4080,8160
Greatest Common Factor
We found the factors 216,8160 . The biggest common factor number is the GCF number.
So the greatest common factor 216,8160 is 24.
Lets's calculate LCM of 645,9890
5 | 645, 9890 |
43 | 129, 1978 |
3, 46 |
∴ So the LCM of the given numbers is 5 x 43 x 3 x 46 = 29670
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/29670
Therefore, the GCF of Fractions 216/645,8160/9890 is 24/29670
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 645,9890 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(645,9890) = 215
common factors(in case of two or more numbers have common factors) = 1
GCF(645,9890) x common factors =215 x 1 = 215
LCM(645,9890) = ( 645 × 9890 ) / 215
LCM(645,9890) = 6379050 / 215
LCM(645,9890) = 29670
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 216/645, 8160/9890?
Answer: GCF of Numerators as per given numbers 216/645, 8160/9890 is
GCF of Numerators i.e. for 216,8160 is 24
LCM of denominators i.e. for 645,9890 is 29670.
Thus, GCF of Fractions is 24/29670.Finally, GCF of Fractions for 216/645, 8160/9890 is 24/29670.