Use our free GCF of Fractions Calculator tool to compute the GCF of 279/234, 105/923 i.e 3/16614 easily. The following is the detailed procedure to determine the greatest common factor of fractions 279/234, 105/923.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 279/234,105/923
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 279/234,105/923, numerators are 279,105
Denominators are 234,923
The GCF of 279,105 is 3 .
LCM of 234,923 is 16614.
The greatest common factor of 279/234,105/923 = [GCF of 279,105]/[LCM of 234,923]= 3/16614
Therefore, the GCF of 279/234,105/923 is 3/16614.
To find the highest common factor of 279,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 279 are 1, 3, 9, 31, 93, 279
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 279,105 is 3.
Lets's calculate GCF of 279,105
3 | 279, 105 |
93, 35 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 279
:1,3,9,31,93,279
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 279,105 . The biggest common factor number is the GCF number.
So the greatest common factor 279,105 is 3.
Lets's calculate LCM of 234,923
13 | 234, 923 |
18, 71 |
∴ So the LCM of the given numbers is 13 x 18 x 71 = 16614
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/16614
Therefore, the GCF of Fractions 279/234,105/923 is 3/16614
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 234,923 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(234,923) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(234,923) x common factors =13 x 1 = 13
LCM(234,923) = ( 234 × 923 ) / 13
LCM(234,923) = 215982 / 13
LCM(234,923) = 16614
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 279,105?
The HCF of 279,105 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 279/234, 105/923?
Answer: GCF of Numerators as per given numbers 279/234, 105/923 is
GCF of Numerators i.e. for 279,105 is 3
LCM of denominators i.e. for 234,923 is 16614.
Thus, GCF of Fractions is 3/16614.Finally, GCF of Fractions for 279/234, 105/923 is 3/16614.