Use our free GCF of Fractions Calculator tool to compute the GCF of 497/512, 566/657 i.e 1/336384 easily. The following is the detailed procedure to determine the greatest common factor of fractions 497/512, 566/657.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 497/512,566/657
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 497/512,566/657, numerators are 497,566
Denominators are 512,657
The GCF of 497,566 is 1 .
LCM of 512,657 is 336384.
The greatest common factor of 497/512,566/657 = [GCF of 497,566]/[LCM of 512,657]= 1/336384
Therefore, the GCF of 497/512,566/657 is 1/336384.
To find the highest common factor of 497,566, we have to find the factors of both numbers and list the highest common factor.
The factors of 497 are 1, 7, 71, 497
The factors of 566 are 1, 2, 283, 566
The HCF of 497,566 is 1.
Lets's calculate GCF of 497,566
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 497
:1,7,71,497
Now, list down the factors of 566
:1,2,283,566
Greatest Common Factor
We found the factors 497,566 . The biggest common factor number is the GCF number.
So the greatest common factor 497,566 is 1.
Lets's calculate LCM of 512,657
Given numbers has no common factors except 1. So, there LCM is their product i.e 336384
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/336384
Therefore, the GCF of Fractions 497/512,566/657 is 1/336384
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 512,657 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,657) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(512,657) x common factors =1 x 1 = 1
LCM(512,657) = ( 512 × 657 ) / 1
LCM(512,657) = 336384 / 1
LCM(512,657) = 336384
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 497,566?
The HCF of 497,566 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 497/512, 566/657?
Answer: GCF of Numerators as per given numbers 497/512, 566/657 is
GCF of Numerators i.e. for 497,566 is 1
LCM of denominators i.e. for 512,657 is 336384.
Thus, GCF of Fractions is 1/336384.Finally, GCF of Fractions for 497/512, 566/657 is 1/336384.