Use our free GCF of Fractions Calculator tool to compute the GCF of 257/723, 217/453 i.e 1/109173 easily. The following is the detailed procedure to determine the greatest common factor of fractions 257/723, 217/453.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 257/723,217/453
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 257/723,217/453, numerators are 257,217
Denominators are 723,453
The GCF of 257,217 is 1 .
LCM of 723,453 is 109173.
The greatest common factor of 257/723,217/453 = [GCF of 257,217]/[LCM of 723,453]= 1/109173
Therefore, the GCF of 257/723,217/453 is 1/109173.
To find the highest common factor of 257,217, we have to find the factors of both numbers and list the highest common factor.
The factors of 257 are 1, 257
The factors of 217 are 1, 7, 31, 217
The HCF of 257,217 is 1.
Lets's calculate GCF of 257,217
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 257
:1,257
Now, list down the factors of 217
:1,7,31,217
Greatest Common Factor
We found the factors 257,217 . The biggest common factor number is the GCF number.
So the greatest common factor 257,217 is 1.
Lets's calculate LCM of 723,453
3 | 723, 453 |
241, 151 |
∴ So the LCM of the given numbers is 3 x 241 x 151 = 109173
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/109173
Therefore, the GCF of Fractions 257/723,217/453 is 1/109173
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 723,453 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(723,453) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(723,453) x common factors =3 x 1 = 3
LCM(723,453) = ( 723 × 453 ) / 3
LCM(723,453) = 327519 / 3
LCM(723,453) = 109173
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 257,217?
The HCF of 257,217 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 257/723, 217/453?
Answer: GCF of Numerators as per given numbers 257/723, 217/453 is
GCF of Numerators i.e. for 257,217 is 1
LCM of denominators i.e. for 723,453 is 109173.
Thus, GCF of Fractions is 1/109173.Finally, GCF of Fractions for 257/723, 217/453 is 1/109173.