Use our free GCF of Fractions Calculator tool to compute the GCF of 217/271, 754/825 i.e 1/223575 easily. The following is the detailed procedure to determine the greatest common factor of fractions 217/271, 754/825.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 217/271,754/825
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 217/271,754/825, numerators are 217,754
Denominators are 271,825
The GCF of 217,754 is 1 .
LCM of 271,825 is 223575.
The greatest common factor of 217/271,754/825 = [GCF of 217,754]/[LCM of 271,825]= 1/223575
Therefore, the GCF of 217/271,754/825 is 1/223575.
To find the highest common factor of 217,754, we have to find the factors of both numbers and list the highest common factor.
The factors of 217 are 1, 7, 31, 217
The factors of 754 are 1, 2, 13, 26, 29, 58, 377, 754
The HCF of 217,754 is 1.
Lets's calculate GCF of 217,754
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 217
:1,7,31,217
Now, list down the factors of 754
:1,2,13,26,29,58,377,754
Greatest Common Factor
We found the factors 217,754 . The biggest common factor number is the GCF number.
So the greatest common factor 217,754 is 1.
Lets's calculate LCM of 271,825
Given numbers has no common factors except 1. So, there LCM is their product i.e 223575
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/223575
Therefore, the GCF of Fractions 217/271,754/825 is 1/223575
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 271,825 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(271,825) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(271,825) x common factors =1 x 1 = 1
LCM(271,825) = ( 271 × 825 ) / 1
LCM(271,825) = 223575 / 1
LCM(271,825) = 223575
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 217,754?
The HCF of 217,754 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 217/271, 754/825?
Answer: GCF of Numerators as per given numbers 217/271, 754/825 is
GCF of Numerators i.e. for 217,754 is 1
LCM of denominators i.e. for 271,825 is 223575.
Thus, GCF of Fractions is 1/223575.Finally, GCF of Fractions for 217/271, 754/825 is 1/223575.