Use our free GCF of Fractions Calculator tool to compute the GCF of 402/854, 405/349 i.e 3/298046 easily. The following is the detailed procedure to determine the greatest common factor of fractions 402/854, 405/349.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 402/854,405/349
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 402/854,405/349, numerators are 402,405
Denominators are 854,349
The GCF of 402,405 is 3 .
LCM of 854,349 is 298046.
The greatest common factor of 402/854,405/349 = [GCF of 402,405]/[LCM of 854,349]= 3/298046
Therefore, the GCF of 402/854,405/349 is 3/298046.
To find the highest common factor of 402,405, we have to find the factors of both numbers and list the highest common factor.
The factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The HCF of 402,405 is 3.
Lets's calculate GCF of 402,405
3 | 402, 405 |
134, 135 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 402
:1,2,3,6,67,134,201,402
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Greatest Common Factor
We found the factors 402,405 . The biggest common factor number is the GCF number.
So the greatest common factor 402,405 is 3.
Lets's calculate LCM of 854,349
Given numbers has no common factors except 1. So, there LCM is their product i.e 298046
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/298046
Therefore, the GCF of Fractions 402/854,405/349 is 3/298046
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 854,349 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(854,349) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(854,349) x common factors =1 x 1 = 1
LCM(854,349) = ( 854 × 349 ) / 1
LCM(854,349) = 298046 / 1
LCM(854,349) = 298046
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 402,405?
The HCF of 402,405 is 3
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 402/854, 405/349?
Answer: GCF of Numerators as per given numbers 402/854, 405/349 is
GCF of Numerators i.e. for 402,405 is 3
LCM of denominators i.e. for 854,349 is 298046.
Thus, GCF of Fractions is 3/298046.Finally, GCF of Fractions for 402/854, 405/349 is 3/298046.