Use our free GCF of Fractions Calculator tool to compute the GCF of 725/470, 109/300 i.e 1/14100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 725/470, 109/300.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 725/470,109/300
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 725/470,109/300, numerators are 725,109
Denominators are 470,300
The GCF of 725,109 is 1 .
LCM of 470,300 is 14100.
The greatest common factor of 725/470,109/300 = [GCF of 725,109]/[LCM of 470,300]= 1/14100
Therefore, the GCF of 725/470,109/300 is 1/14100.
To find the highest common factor of 725,109, 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 109 are 1, 109
The HCF of 725,109 is 1.
Lets's calculate GCF of 725,109
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 725
:1,5,25,29,145,725
Now, list down the factors of 109
:1,109
Greatest Common Factor
We found the factors 725,109 . The biggest common factor number is the GCF number.
So the greatest common factor 725,109 is 1.
Lets's calculate LCM of 470,300
2 | 470, 300 |
5 | 235, 150 |
47, 30 |
∴ So the LCM of the given numbers is 2 x 5 x 47 x 30 = 14100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/14100
Therefore, the GCF of Fractions 725/470,109/300 is 1/14100
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 470,300 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(470,300) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(470,300) x common factors =10 x 1 = 10
LCM(470,300) = ( 470 × 300 ) / 10
LCM(470,300) = 141000 / 10
LCM(470,300) = 14100
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 725,109?
The HCF of 725,109 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 725/470, 109/300?
Answer: GCF of Numerators as per given numbers 725/470, 109/300 is
GCF of Numerators i.e. for 725,109 is 1
LCM of denominators i.e. for 470,300 is 14100.
Thus, GCF of Fractions is 1/14100.Finally, GCF of Fractions for 725/470, 109/300 is 1/14100.