Use our free GCF of Fractions Calculator tool to compute the GCF of 125/925, 975/814 i.e 25/20350 easily. The following is the detailed procedure to determine the greatest common factor of fractions 125/925, 975/814.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 125/925,975/814
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 125/925,975/814, numerators are 125,975
Denominators are 925,814
The GCF of 125,975 is 25 .
LCM of 925,814 is 20350.
The greatest common factor of 125/925,975/814 = [GCF of 125,975]/[LCM of 925,814]= 25/20350
Therefore, the GCF of 125/925,975/814 is 25/20350.
To find the highest common factor of 125,975, we have to find the factors of both numbers and list the highest common factor.
The factors of 125 are 1, 5, 25, 125
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The HCF of 125,975 is 25.
Lets's calculate GCF of 125,975
5 | 125, 975 |
5 | 25, 195 |
5, 39 |
∴ So the GCF of the given numbers is 5 x 5 = 25
Now, list down the factors of 125
:1,5,25,125
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Greatest Common Factor
We found the factors 125,975 . The biggest common factor number is the GCF number.
So the greatest common factor 125,975 is 25.
Lets's calculate LCM of 925,814
37 | 925, 814 |
25, 22 |
∴ So the LCM of the given numbers is 37 x 25 x 22 = 20350
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 25/20350
Therefore, the GCF of Fractions 125/925,975/814 is 25/20350
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 925,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(925,814) = 37
common factors(in case of two or more numbers have common factors) = 1
GCF(925,814) x common factors =37 x 1 = 37
LCM(925,814) = ( 925 × 814 ) / 37
LCM(925,814) = 752950 / 37
LCM(925,814) = 20350
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 125,975?
The HCF of 125,975 is 25
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 125/925, 975/814?
Answer: GCF of Numerators as per given numbers 125/925, 975/814 is
GCF of Numerators i.e. for 125,975 is 25
LCM of denominators i.e. for 925,814 is 20350.
Thus, GCF of Fractions is 25/20350.Finally, GCF of Fractions for 125/925, 975/814 is 25/20350.