Use our free GCF of Fractions Calculator tool to compute the GCF of 23/340, 33/260, 164/697 i.e 1/181220 easily. The following is the detailed procedure to determine the greatest common factor of fractions 23/340, 33/260, 164/697.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 23/340,33/260,164/697
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 23/340,33/260,164/697, numerators are 23,33,164
Denominators are 340,260,697
The GCF of 23,33,164 is 1 .
LCM of 340,260,697 is 181220.
The greatest common factor of 23/340,33/260,164/697 = [GCF of 23,33,164]/[LCM of 340,260,697]= 1/181220
Therefore, the GCF of 23/340,33/260,164/697 is 1/181220.
To find the highest common factor of 23,33,164, we have to find the factors of both numbers and list the highest common factor.
The factors of 23 are 1, 23
The factors of 33 are 1, 3, 11, 33
The factors of 164 are 1, 2, 4, 41, 82, 164
The HCF of 23,33,164 is 1.
Lets's calculate GCF of 23,33,164
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 23
:1,23
Now, list down the factors of 33
:1,3,11,33
Now, list down the factors of 164
:1,2,4,41,82,164
Greatest Common Factor
We found the factors 23,33,164 . The biggest common factor number is the GCF number.
So the greatest common factor 23,33,164 is 1.
Lets's calculate LCM of 340,260,697
2 | 340, 260, 697 |
2 | 170, 130, 697 |
5 | 85, 65, 697 |
17 | 17, 13, 697 |
1, 13, 41 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 17 x 1 x 13 x 41 = 181220
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/181220
Therefore, the GCF of Fractions 23/340,33/260,164/697 is 1/181220
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 340,260,697 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(340,260,697) = 1
common factors(in case of two or more numbers have common factors) = 340
GCF(340,260,697) x common factors =1 x 340 = 340
LCM(340,260,697) = ( 340 × 260 × 697 ) / 340
LCM(340,260,697) = 61614800 / 340
LCM(340,260,697) = 181220
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 23,33,164?
The HCF of 23,33,164 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 23/340, 33/260, 164/697?
Answer: GCF of Numerators as per given numbers 23/340, 33/260, 164/697 is
GCF of Numerators i.e. for 23,33,164 is 1
LCM of denominators i.e. for 340,260,697 is 181220.
Thus, GCF of Fractions is 1/181220.Finally, GCF of Fractions for 23/340, 33/260, 164/697 is 1/181220.