Use our free GCF of Fractions Calculator tool to compute the GCF of 854/633, 408/208 i.e 2/131664 easily. The following is the detailed procedure to determine the greatest common factor of fractions 854/633, 408/208.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 854/633,408/208
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 854/633,408/208, numerators are 854,408
Denominators are 633,208
The GCF of 854,408 is 2 .
LCM of 633,208 is 131664.
The greatest common factor of 854/633,408/208 = [GCF of 854,408]/[LCM of 633,208]= 2/131664
Therefore, the GCF of 854/633,408/208 is 2/131664.
To find the highest common factor of 854,408, we have to find the factors of both numbers and list the highest common factor.
The factors of 854 are 1, 2, 7, 14, 61, 122, 427, 854
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The HCF of 854,408 is 2.
Lets's calculate GCF of 854,408
2 | 854, 408 |
427, 204 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 854
:1,2,7,14,61,122,427,854
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Greatest Common Factor
We found the factors 854,408 . The biggest common factor number is the GCF number.
So the greatest common factor 854,408 is 2.
Lets's calculate LCM of 633,208
Given numbers has no common factors except 1. So, there LCM is their product i.e 131664
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/131664
Therefore, the GCF of Fractions 854/633,408/208 is 2/131664
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 633,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(633,208) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(633,208) x common factors =1 x 1 = 1
LCM(633,208) = ( 633 × 208 ) / 1
LCM(633,208) = 131664 / 1
LCM(633,208) = 131664
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 854,408?
The HCF of 854,408 is 2
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 854/633, 408/208?
Answer: GCF of Numerators as per given numbers 854/633, 408/208 is
GCF of Numerators i.e. for 854,408 is 2
LCM of denominators i.e. for 633,208 is 131664.
Thus, GCF of Fractions is 2/131664.Finally, GCF of Fractions for 854/633, 408/208 is 2/131664.