Use our free GCF of Fractions Calculator tool to compute the GCF of 725/271, 440/409 i.e 5/110839 easily. The following is the detailed procedure to determine the greatest common factor of fractions 725/271, 440/409.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 725/271,440/409
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 725/271,440/409, numerators are 725,440
Denominators are 271,409
The GCF of 725,440 is 5 .
LCM of 271,409 is 110839.
The greatest common factor of 725/271,440/409 = [GCF of 725,440]/[LCM of 271,409]= 5/110839
Therefore, the GCF of 725/271,440/409 is 5/110839.
To find the highest common factor of 725,440, we have to find the factors of both numbers and list the highest common factor.
The factors of 725 are 1, 5, 25, 29, 145, 725
The factors of 440 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440
The HCF of 725,440 is 5.
Lets's calculate GCF of 725,440
5 | 725, 440 |
145, 88 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 725
:1,5,25,29,145,725
Now, list down the factors of 440
:1,2,4,5,8,10,11,20,22,40,44,55,88,110,220,440
Greatest Common Factor
We found the factors 725,440 . The biggest common factor number is the GCF number.
So the greatest common factor 725,440 is 5.
Lets's calculate LCM of 271,409
Given numbers has no common factors except 1. So, there LCM is their product i.e 110839
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/110839
Therefore, the GCF of Fractions 725/271,440/409 is 5/110839
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 271,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(271,409) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(271,409) x common factors =1 x 1 = 1
LCM(271,409) = ( 271 × 409 ) / 1
LCM(271,409) = 110839 / 1
LCM(271,409) = 110839
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 725,440?
The HCF of 725,440 is 5
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 725/271, 440/409?
Answer: GCF of Numerators as per given numbers 725/271, 440/409 is
GCF of Numerators i.e. for 725,440 is 5
LCM of denominators i.e. for 271,409 is 110839.
Thus, GCF of Fractions is 5/110839.Finally, GCF of Fractions for 725/271, 440/409 is 5/110839.