Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 814/827,5180/249
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 814,5180
Greatest Common Factor of Numerators i.e. GCF of 814,5180 is 74 .
LCM of Denominators means LCM of 827,249 as per the given fractions.
LCM of 827,249 is 205923 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 814,5180
2 | 814, 5180 |
37 | 407, 2590 |
11, 70 |
∴ So the GCF of the given numbers is 2 x 37 = 74
Factors of 814
List of positive integer factors of 814 that divides 814 without a remainder.
1,2,11,22,37,74,407,814
Factors of 5180
List of positive integer factors of 5180 that divides 5180 without a remainder.
1,2,4,5,7,10,14,20,28,35,37,70,74,140,148,185,259,370,518,740,1036,1295,2590,5180
Greatest Common Factor
We found the factors 814,5180 . The biggest common factor number is the GCF number.
So the greatest common factor 814,5180 is 74.
Lets's calculate LCM of 827,249
Given numbers has no common factors except 1. So, there LCM is their product i.e 205923
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 74/205923
Therefore, the GCF of Fractions 814/827,5180/249 is 74/205923
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 827,249 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(827,249) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(827,249) x common factors =1 x 1 = 1
LCM(827,249) = ( 827 × 249 ) / 1
LCM(827,249) = 205923 / 1
LCM(827,249) = 205923
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 814/827, 5180/249?
Answer: GCF of Numerators as per given numbers 814/827, 5180/249 is
GCF of Numerators i.e. for 814,5180 is 74
LCM of denominators i.e. for 827,249 is 205923.
Thus, GCF of Fractions is 74/205923.Finally, GCF of Fractions for 814/827, 5180/249 is 74/205923.