Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 299/53,708/45,209/441
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 299,708,209
Greatest Common Factor of Numerators i.e. GCF of 299,708,209 is 1 .
LCM of Denominators means LCM of 53,45,441 as per the given fractions.
LCM of 53,45,441 is 116865 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 299,708,209
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 299
List of positive integer factors of 299 that divides 299 without a remainder.
1,13,23,299
Factors of 708
List of positive integer factors of 708 that divides 708 without a remainder.
1,2,3,4,6,12,59,118,177,236,354,708
Factors of 209
List of positive integer factors of 209 that divides 209 without a remainder.
1,11,19,209
Greatest Common Factor
We found the factors 299,708,209 . The biggest common factor number is the GCF number.
So the greatest common factor 299,708,209 is 1.
Lets's calculate LCM of 53,45,441
3 | 53, 45, 441 |
3 | 53, 15, 147 |
53, 5, 49 |
∴ So the LCM of the given numbers is 3 x 3 x 53 x 5 x 49 = 116865
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/116865
Therefore, the GCF of Fractions 299/53,708/45,209/441 is 1/116865
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 53,45,441 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(53,45,441) = 1
common factors(in case of two or more numbers have common factors) = 9
GCF(53,45,441) x common factors =1 x 9 = 9
LCM(53,45,441) = ( 53 × 45 × 441 ) / 9
LCM(53,45,441) = 1051785 / 9
LCM(53,45,441) = 116865
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 299/53, 708/45, 209/441?
Answer: GCF of Numerators as per given numbers 299/53, 708/45, 209/441 is
GCF of Numerators i.e. for 299,708,209 is 1
LCM of denominators i.e. for 53,45,441 is 116865.
Thus, GCF of Fractions is 1/116865.Finally, GCF of Fractions for 299/53, 708/45, 209/441 is 1/116865.