Use our free GCF of Fractions Calculator tool to compute the GCF of 344/172, 664/259 i.e 8/44548 easily. The following is the detailed procedure to determine the greatest common factor of fractions 344/172, 664/259.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 344/172,664/259
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 344/172,664/259, numerators are 344,664
Denominators are 172,259
The GCF of 344,664 is 8 .
LCM of 172,259 is 44548.
The greatest common factor of 344/172,664/259 = [GCF of 344,664]/[LCM of 172,259]= 8/44548
Therefore, the GCF of 344/172,664/259 is 8/44548.
To find the highest common factor of 344,664, we have to find the factors of both numbers and list the highest common factor.
The factors of 344 are 1, 2, 4, 8, 43, 86, 172, 344
The factors of 664 are 1, 2, 4, 8, 83, 166, 332, 664
The HCF of 344,664 is 8.
Lets's calculate GCF of 344,664
2 | 344, 664 |
2 | 172, 332 |
2 | 86, 166 |
43, 83 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 344
:1,2,4,8,43,86,172,344
Now, list down the factors of 664
:1,2,4,8,83,166,332,664
Greatest Common Factor
We found the factors 344,664 . The biggest common factor number is the GCF number.
So the greatest common factor 344,664 is 8.
Lets's calculate LCM of 172,259
Given numbers has no common factors except 1. So, there LCM is their product i.e 44548
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/44548
Therefore, the GCF of Fractions 344/172,664/259 is 8/44548
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 172,259 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(172,259) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(172,259) x common factors =1 x 1 = 1
LCM(172,259) = ( 172 × 259 ) / 1
LCM(172,259) = 44548 / 1
LCM(172,259) = 44548
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 344,664?
The HCF of 344,664 is 8
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 344/172, 664/259?
Answer: GCF of Numerators as per given numbers 344/172, 664/259 is
GCF of Numerators i.e. for 344,664 is 8
LCM of denominators i.e. for 172,259 is 44548.
Thus, GCF of Fractions is 8/44548.Finally, GCF of Fractions for 344/172, 664/259 is 8/44548.