Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 214/52,120/1699
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 214,120
Greatest Common Factor of Numerators i.e. GCF of 214,120 is 2 .
LCM of Denominators means LCM of 52,1699 as per the given fractions.
LCM of 52,1699 is 88348 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 214,120
2 | 214, 120 |
107, 60 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 214
List of positive integer factors of 214 that divides 214 without a remainder.
1,2,107,214
Factors of 120
List of positive integer factors of 120 that divides 120 without a remainder.
1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 214,120 . The biggest common factor number is the GCF number.
So the greatest common factor 214,120 is 2.
Lets's calculate LCM of 52,1699
Given numbers has no common factors except 1. So, there LCM is their product i.e 88348
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/88348
Therefore, the GCF of Fractions 214/52,120/1699 is 2/88348
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 52,1699 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(52,1699) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(52,1699) x common factors =1 x 1 = 1
LCM(52,1699) = ( 52 × 1699 ) / 1
LCM(52,1699) = 88348 / 1
LCM(52,1699) = 88348
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 214/52, 120/1699?
Answer: GCF of Numerators as per given numbers 214/52, 120/1699 is
GCF of Numerators i.e. for 214,120 is 2
LCM of denominators i.e. for 52,1699 is 88348.
Thus, GCF of Fractions is 2/88348.Finally, GCF of Fractions for 214/52, 120/1699 is 2/88348.