Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 106/34,410/1292
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 106,410
Greatest Common Factor of Numerators i.e. GCF of 106,410 is 2 .
LCM of Denominators means LCM of 34,1292 as per the given fractions.
LCM of 34,1292 is 1292 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 106,410
2 | 106, 410 |
53, 205 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 106
List of positive integer factors of 106 that divides 106 without a remainder.
1,2,53,106
Factors of 410
List of positive integer factors of 410 that divides 410 without a remainder.
1,2,5,10,41,82,205,410
Greatest Common Factor
We found the factors 106,410 . The biggest common factor number is the GCF number.
So the greatest common factor 106,410 is 2.
Lets's calculate LCM of 34,1292
2 | 34, 1292 |
17 | 17, 646 |
1, 38 |
∴ So the LCM of the given numbers is 2 x 17 x 1 x 38 = 1292
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1292
Therefore, the GCF of Fractions 106/34,410/1292 is 2/1292
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 34,1292 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,1292) = 34
common factors(in case of two or more numbers have common factors) = 1
GCF(34,1292) x common factors =34 x 1 = 34
LCM(34,1292) = ( 34 × 1292 ) / 34
LCM(34,1292) = 43928 / 34
LCM(34,1292) = 1292
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 106/34, 410/1292?
Answer: GCF of Numerators as per given numbers 106/34, 410/1292 is
GCF of Numerators i.e. for 106,410 is 2
LCM of denominators i.e. for 34,1292 is 1292.
Thus, GCF of Fractions is 2/1292.Finally, GCF of Fractions for 106/34, 410/1292 is 2/1292.