Use our free GCF of Fractions Calculator tool to compute the GCF of 287/478, 658/440 i.e 7/105160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 287/478, 658/440.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 287/478,658/440
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 287/478,658/440, numerators are 287,658
Denominators are 478,440
The GCF of 287,658 is 7 .
LCM of 478,440 is 105160.
The greatest common factor of 287/478,658/440 = [GCF of 287,658]/[LCM of 478,440]= 7/105160
Therefore, the GCF of 287/478,658/440 is 7/105160.
To find the highest common factor of 287,658, we have to find the factors of both numbers and list the highest common factor.
The factors of 287 are 1, 7, 41, 287
The factors of 658 are 1, 2, 7, 14, 47, 94, 329, 658
The HCF of 287,658 is 7.
Lets's calculate GCF of 287,658
7 | 287, 658 |
41, 94 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 287
:1,7,41,287
Now, list down the factors of 658
:1,2,7,14,47,94,329,658
Greatest Common Factor
We found the factors 287,658 . The biggest common factor number is the GCF number.
So the greatest common factor 287,658 is 7.
Lets's calculate LCM of 478,440
2 | 478, 440 |
239, 220 |
∴ So the LCM of the given numbers is 2 x 239 x 220 = 105160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/105160
Therefore, the GCF of Fractions 287/478,658/440 is 7/105160
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 478,440 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(478,440) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(478,440) x common factors =2 x 1 = 2
LCM(478,440) = ( 478 × 440 ) / 2
LCM(478,440) = 210320 / 2
LCM(478,440) = 105160
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 287,658?
The HCF of 287,658 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 287/478, 658/440?
Answer: GCF of Numerators as per given numbers 287/478, 658/440 is
GCF of Numerators i.e. for 287,658 is 7
LCM of denominators i.e. for 478,440 is 105160.
Thus, GCF of Fractions is 7/105160.Finally, GCF of Fractions for 287/478, 658/440 is 7/105160.