Use our free GCF of Fractions Calculator tool to compute the GCF of 59/406, 410/833, 684/204 i.e 1/289884 easily. The following is the detailed procedure to determine the greatest common factor of fractions 59/406, 410/833, 684/204.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 59/406,410/833,684/204
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 59/406,410/833,684/204, numerators are 59,410,684
Denominators are 406,833,204
The GCF of 59,410,684 is 1 .
LCM of 406,833,204 is 289884.
The greatest common factor of 59/406,410/833,684/204 = [GCF of 59,410,684]/[LCM of 406,833,204]= 1/289884
Therefore, the GCF of 59/406,410/833,684/204 is 1/289884.
To find the highest common factor of 59,410,684, we have to find the factors of both numbers and list the highest common factor.
The factors of 59 are 1, 59
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 59,410,684 is 1.
Lets's calculate GCF of 59,410,684
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 59
:1,59
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 59,410,684 . The biggest common factor number is the GCF number.
So the greatest common factor 59,410,684 is 1.
Lets's calculate LCM of 406,833,204
2 | 406, 833, 204 |
7 | 203, 833, 102 |
17 | 29, 119, 102 |
29, 7, 6 |
∴ So the LCM of the given numbers is 2 x 7 x 17 x 29 x 7 x 6 = 289884
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/289884
Therefore, the GCF of Fractions 59/406,410/833,684/204 is 1/289884
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 406,833,204 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(406,833,204) = 1
common factors(in case of two or more numbers have common factors) = 238
GCF(406,833,204) x common factors =1 x 238 = 238
LCM(406,833,204) = ( 406 × 833 × 204 ) / 238
LCM(406,833,204) = 68992392 / 238
LCM(406,833,204) = 289884
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 59,410,684?
The HCF of 59,410,684 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. 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.
4. What is the GCF of Fractions for 59/406, 410/833, 684/204?
Answer: GCF of Numerators as per given numbers 59/406, 410/833, 684/204 is
GCF of Numerators i.e. for 59,410,684 is 1
LCM of denominators i.e. for 406,833,204 is 289884.
Thus, GCF of Fractions is 1/289884.Finally, GCF of Fractions for 59/406, 410/833, 684/204 is 1/289884.