Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 784/36,406/8246
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 784,406
Greatest Common Factor of Numerators i.e. GCF of 784,406 is 14 .
LCM of Denominators means LCM of 36,8246 as per the given fractions.
LCM of 36,8246 is 148428 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 784,406
2 | 784, 406 |
7 | 392, 203 |
56, 29 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Factors of 784
List of positive integer factors of 784 that divides 784 without a remainder.
1,2,4,7,8,14,16,28,49,56,98,112,196,392,784
Factors of 406
List of positive integer factors of 406 that divides 406 without a remainder.
1,2,7,14,29,58,203,406
Greatest Common Factor
We found the factors 784,406 . The biggest common factor number is the GCF number.
So the greatest common factor 784,406 is 14.
Lets's calculate LCM of 36,8246
2 | 36, 8246 |
18, 4123 |
∴ So the LCM of the given numbers is 2 x 18 x 4123 = 148428
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/148428
Therefore, the GCF of Fractions 784/36,406/8246 is 14/148428
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 36,8246 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(36,8246) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(36,8246) x common factors =2 x 1 = 2
LCM(36,8246) = ( 36 × 8246 ) / 2
LCM(36,8246) = 296856 / 2
LCM(36,8246) = 148428
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 784/36, 406/8246?
Answer: GCF of Numerators as per given numbers 784/36, 406/8246 is
GCF of Numerators i.e. for 784,406 is 14
LCM of denominators i.e. for 36,8246 is 148428.
Thus, GCF of Fractions is 14/148428.Finally, GCF of Fractions for 784/36, 406/8246 is 14/148428.