Use our free GCF of Fractions Calculator tool to compute the GCF of 735/314, 205/997 i.e 5/313058 easily. The following is the detailed procedure to determine the greatest common factor of fractions 735/314, 205/997.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 735/314,205/997
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 735/314,205/997, numerators are 735,205
Denominators are 314,997
The GCF of 735,205 is 5 .
LCM of 314,997 is 313058.
The greatest common factor of 735/314,205/997 = [GCF of 735,205]/[LCM of 314,997]= 5/313058
Therefore, the GCF of 735/314,205/997 is 5/313058.
To find the highest common factor of 735,205, we have to find the factors of both numbers and list the highest common factor.
The factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
The factors of 205 are 1, 5, 41, 205
The HCF of 735,205 is 5.
Lets's calculate GCF of 735,205
5 | 735, 205 |
147, 41 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 735
:1,3,5,7,15,21,35,49,105,147,245,735
Now, list down the factors of 205
:1,5,41,205
Greatest Common Factor
We found the factors 735,205 . The biggest common factor number is the GCF number.
So the greatest common factor 735,205 is 5.
Lets's calculate LCM of 314,997
Given numbers has no common factors except 1. So, there LCM is their product i.e 313058
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/313058
Therefore, the GCF of Fractions 735/314,205/997 is 5/313058
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 314,997 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(314,997) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(314,997) x common factors =1 x 1 = 1
LCM(314,997) = ( 314 × 997 ) / 1
LCM(314,997) = 313058 / 1
LCM(314,997) = 313058
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 735,205?
The HCF of 735,205 is 5
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 735/314, 205/997?
Answer: GCF of Numerators as per given numbers 735/314, 205/997 is
GCF of Numerators i.e. for 735,205 is 5
LCM of denominators i.e. for 314,997 is 313058.
Thus, GCF of Fractions is 5/313058.Finally, GCF of Fractions for 735/314, 205/997 is 5/313058.