Use our free GCF of Fractions Calculator tool to compute the GCF of 497/314, 658/936 i.e 7/146952 easily. The following is the detailed procedure to determine the greatest common factor of fractions 497/314, 658/936.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 497/314,658/936
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 497/314,658/936, numerators are 497,658
Denominators are 314,936
The GCF of 497,658 is 7 .
LCM of 314,936 is 146952.
The greatest common factor of 497/314,658/936 = [GCF of 497,658]/[LCM of 314,936]= 7/146952
Therefore, the GCF of 497/314,658/936 is 7/146952.
To find the highest common factor of 497,658, we have to find the factors of both numbers and list the highest common factor.
The factors of 497 are 1, 7, 71, 497
The factors of 658 are 1, 2, 7, 14, 47, 94, 329, 658
The HCF of 497,658 is 7.
Lets's calculate GCF of 497,658
7 | 497, 658 |
71, 94 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 497
:1,7,71,497
Now, list down the factors of 658
:1,2,7,14,47,94,329,658
Greatest Common Factor
We found the factors 497,658 . The biggest common factor number is the GCF number.
So the greatest common factor 497,658 is 7.
Lets's calculate LCM of 314,936
2 | 314, 936 |
157, 468 |
∴ So the LCM of the given numbers is 2 x 157 x 468 = 146952
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/146952
Therefore, the GCF of Fractions 497/314,658/936 is 7/146952
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 314,936 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(314,936) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(314,936) x common factors =2 x 1 = 2
LCM(314,936) = ( 314 × 936 ) / 2
LCM(314,936) = 293904 / 2
LCM(314,936) = 146952
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 497,658?
The HCF of 497,658 is 7
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 497/314, 658/936?
Answer: GCF of Numerators as per given numbers 497/314, 658/936 is
GCF of Numerators i.e. for 497,658 is 7
LCM of denominators i.e. for 314,936 is 146952.
Thus, GCF of Fractions is 7/146952.Finally, GCF of Fractions for 497/314, 658/936 is 7/146952.