Use our free GCF of Fractions Calculator tool to compute the GCF of 133/320, 164/674 i.e 1/107840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 133/320, 164/674.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 133/320,164/674
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 133/320,164/674, numerators are 133,164
Denominators are 320,674
The GCF of 133,164 is 1 .
LCM of 320,674 is 107840.
The greatest common factor of 133/320,164/674 = [GCF of 133,164]/[LCM of 320,674]= 1/107840
Therefore, the GCF of 133/320,164/674 is 1/107840.
To find the highest common factor of 133,164, we have to find the factors of both numbers and list the highest common factor.
The factors of 133 are 1, 7, 19, 133
The factors of 164 are 1, 2, 4, 41, 82, 164
The HCF of 133,164 is 1.
Lets's calculate GCF of 133,164
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 133
:1,7,19,133
Now, list down the factors of 164
:1,2,4,41,82,164
Greatest Common Factor
We found the factors 133,164 . The biggest common factor number is the GCF number.
So the greatest common factor 133,164 is 1.
Lets's calculate LCM of 320,674
2 | 320, 674 |
160, 337 |
∴ So the LCM of the given numbers is 2 x 160 x 337 = 107840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/107840
Therefore, the GCF of Fractions 133/320,164/674 is 1/107840
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 320,674 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(320,674) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(320,674) x common factors =2 x 1 = 2
LCM(320,674) = ( 320 × 674 ) / 2
LCM(320,674) = 215680 / 2
LCM(320,674) = 107840
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 133,164?
The HCF of 133,164 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 133/320, 164/674?
Answer: GCF of Numerators as per given numbers 133/320, 164/674 is
GCF of Numerators i.e. for 133,164 is 1
LCM of denominators i.e. for 320,674 is 107840.
Thus, GCF of Fractions is 1/107840.Finally, GCF of Fractions for 133/320, 164/674 is 1/107840.