Use our free GCF of Fractions Calculator tool to compute the GCF of 667/413, 428/405 i.e 1/167265 easily. The following is the detailed procedure to determine the greatest common factor of fractions 667/413, 428/405.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 667/413,428/405
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 667/413,428/405, numerators are 667,428
Denominators are 413,405
The GCF of 667,428 is 1 .
LCM of 413,405 is 167265.
The greatest common factor of 667/413,428/405 = [GCF of 667,428]/[LCM of 413,405]= 1/167265
Therefore, the GCF of 667/413,428/405 is 1/167265.
To find the highest common factor of 667,428, we have to find the factors of both numbers and list the highest common factor.
The factors of 667 are 1, 23, 29, 667
The factors of 428 are 1, 2, 4, 107, 214, 428
The HCF of 667,428 is 1.
Lets's calculate GCF of 667,428
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 667
:1,23,29,667
Now, list down the factors of 428
:1,2,4,107,214,428
Greatest Common Factor
We found the factors 667,428 . The biggest common factor number is the GCF number.
So the greatest common factor 667,428 is 1.
Lets's calculate LCM of 413,405
Given numbers has no common factors except 1. So, there LCM is their product i.e 167265
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/167265
Therefore, the GCF of Fractions 667/413,428/405 is 1/167265
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 413,405 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(413,405) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(413,405) x common factors =1 x 1 = 1
LCM(413,405) = ( 413 × 405 ) / 1
LCM(413,405) = 167265 / 1
LCM(413,405) = 167265
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 667,428?
The HCF of 667,428 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 667/413, 428/405?
Answer: GCF of Numerators as per given numbers 667/413, 428/405 is
GCF of Numerators i.e. for 667,428 is 1
LCM of denominators i.e. for 413,405 is 167265.
Thus, GCF of Fractions is 1/167265.Finally, GCF of Fractions for 667/413, 428/405 is 1/167265.