Use our free GCF of Fractions Calculator tool to compute the GCF of 33/258, 68/669, 174/509 i.e 1/29284806 easily. The following is the detailed procedure to determine the greatest common factor of fractions 33/258, 68/669, 174/509.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 33/258,68/669,174/509
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 33/258,68/669,174/509, numerators are 33,68,174
Denominators are 258,669,509
The GCF of 33,68,174 is 1 .
LCM of 258,669,509 is 29284806.
The greatest common factor of 33/258,68/669,174/509 = [GCF of 33,68,174]/[LCM of 258,669,509]= 1/29284806
Therefore, the GCF of 33/258,68/669,174/509 is 1/29284806.
To find the highest common factor of 33,68,174, we have to find the factors of both numbers and list the highest common factor.
The factors of 33 are 1, 3, 11, 33
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174
The HCF of 33,68,174 is 1.
Lets's calculate GCF of 33,68,174
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 33
:1,3,11,33
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 174
:1,2,3,6,29,58,87,174
Greatest Common Factor
We found the factors 33,68,174 . The biggest common factor number is the GCF number.
So the greatest common factor 33,68,174 is 1.
Lets's calculate LCM of 258,669,509
3 | 258, 669, 509 |
86, 223, 509 |
∴ So the LCM of the given numbers is 3 x 86 x 223 x 509 = 29284806
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/29284806
Therefore, the GCF of Fractions 33/258,68/669,174/509 is 1/29284806
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 258,669,509 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(258,669,509) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(258,669,509) x common factors =1 x 3 = 3
LCM(258,669,509) = ( 258 × 669 × 509 ) / 3
LCM(258,669,509) = 87854418 / 3
LCM(258,669,509) = 29284806
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 33,68,174?
The HCF of 33,68,174 is 1
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 33/258, 68/669, 174/509?
Answer: GCF of Numerators as per given numbers 33/258, 68/669, 174/509 is
GCF of Numerators i.e. for 33,68,174 is 1
LCM of denominators i.e. for 258,669,509 is 29284806.
Thus, GCF of Fractions is 1/29284806.Finally, GCF of Fractions for 33/258, 68/669, 174/509 is 1/29284806.