Use our free GCF of Fractions Calculator tool to compute the GCF of 403/325, 217/971 i.e 31/315575 easily. The following is the detailed procedure to determine the greatest common factor of fractions 403/325, 217/971.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 403/325,217/971
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 403/325,217/971, numerators are 403,217
Denominators are 325,971
The GCF of 403,217 is 31 .
LCM of 325,971 is 315575.
The greatest common factor of 403/325,217/971 = [GCF of 403,217]/[LCM of 325,971]= 31/315575
Therefore, the GCF of 403/325,217/971 is 31/315575.
To find the highest common factor of 403,217, we have to find the factors of both numbers and list the highest common factor.
The factors of 403 are 1, 13, 31, 403
The factors of 217 are 1, 7, 31, 217
The HCF of 403,217 is 31.
Lets's calculate GCF of 403,217
31 | 403, 217 |
13, 7 |
∴ So the GCF of the given numbers is 31 = 31
Now, list down the factors of 403
:1,13,31,403
Now, list down the factors of 217
:1,7,31,217
Greatest Common Factor
We found the factors 403,217 . The biggest common factor number is the GCF number.
So the greatest common factor 403,217 is 31.
Lets's calculate LCM of 325,971
Given numbers has no common factors except 1. So, there LCM is their product i.e 315575
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/315575
Therefore, the GCF of Fractions 403/325,217/971 is 31/315575
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 325,971 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(325,971) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(325,971) x common factors =1 x 1 = 1
LCM(325,971) = ( 325 × 971 ) / 1
LCM(325,971) = 315575 / 1
LCM(325,971) = 315575
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 403,217?
The HCF of 403,217 is 31
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 403/325, 217/971?
Answer: GCF of Numerators as per given numbers 403/325, 217/971 is
GCF of Numerators i.e. for 403,217 is 31
LCM of denominators i.e. for 325,971 is 315575.
Thus, GCF of Fractions is 31/315575.Finally, GCF of Fractions for 403/325, 217/971 is 31/315575.