Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 214/87,385/52,805/120
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 214,385,805
Greatest Common Factor of Numerators i.e. GCF of 214,385,805 is 1 .
LCM of Denominators means LCM of 87,52,120 as per the given fractions.
LCM of 87,52,120 is 45240 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 214,385,805
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 214
List of positive integer factors of 214 that divides 214 without a remainder.
1,2,107,214
Factors of 385
List of positive integer factors of 385 that divides 385 without a remainder.
1,5,7,11,35,55,77,385
Factors of 805
List of positive integer factors of 805 that divides 805 without a remainder.
1,5,7,23,35,115,161,805
Greatest Common Factor
We found the factors 214,385,805 . The biggest common factor number is the GCF number.
So the greatest common factor 214,385,805 is 1.
Lets's calculate LCM of 87,52,120
2 | 87, 52, 120 |
2 | 87, 26, 60 |
3 | 87, 13, 30 |
29, 13, 10 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 29 x 13 x 10 = 45240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/45240
Therefore, the GCF of Fractions 214/87,385/52,805/120 is 1/45240
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 87,52,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(87,52,120) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(87,52,120) x common factors =1 x 12 = 12
LCM(87,52,120) = ( 87 × 52 × 120 ) / 12
LCM(87,52,120) = 542880 / 12
LCM(87,52,120) = 45240
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 214/87, 385/52, 805/120?
Answer: GCF of Numerators as per given numbers 214/87, 385/52, 805/120 is
GCF of Numerators i.e. for 214,385,805 is 1
LCM of denominators i.e. for 87,52,120 is 45240.
Thus, GCF of Fractions is 1/45240.Finally, GCF of Fractions for 214/87, 385/52, 805/120 is 1/45240.