Use our free GCF of Fractions Calculator tool to compute the GCF of 430/920, 725/610 i.e 5/56120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 430/920, 725/610.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 430/920,725/610
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 430/920,725/610, numerators are 430,725
Denominators are 920,610
The GCF of 430,725 is 5 .
LCM of 920,610 is 56120.
The greatest common factor of 430/920,725/610 = [GCF of 430,725]/[LCM of 920,610]= 5/56120
Therefore, the GCF of 430/920,725/610 is 5/56120.
To find the highest common factor of 430,725, we have to find the factors of both numbers and list the highest common factor.
The factors of 430 are 1, 2, 5, 10, 43, 86, 215, 430
The factors of 725 are 1, 5, 25, 29, 145, 725
The HCF of 430,725 is 5.
Lets's calculate GCF of 430,725
5 | 430, 725 |
86, 145 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 430
:1,2,5,10,43,86,215,430
Now, list down the factors of 725
:1,5,25,29,145,725
Greatest Common Factor
We found the factors 430,725 . The biggest common factor number is the GCF number.
So the greatest common factor 430,725 is 5.
Lets's calculate LCM of 920,610
2 | 920, 610 |
5 | 460, 305 |
92, 61 |
∴ So the LCM of the given numbers is 2 x 5 x 92 x 61 = 56120
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/56120
Therefore, the GCF of Fractions 430/920,725/610 is 5/56120
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 920,610 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(920,610) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(920,610) x common factors =10 x 1 = 10
LCM(920,610) = ( 920 × 610 ) / 10
LCM(920,610) = 561200 / 10
LCM(920,610) = 56120
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 430,725?
The HCF of 430,725 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 430/920, 725/610?
Answer: GCF of Numerators as per given numbers 430/920, 725/610 is
GCF of Numerators i.e. for 430,725 is 5
LCM of denominators i.e. for 920,610 is 56120.
Thus, GCF of Fractions is 5/56120.Finally, GCF of Fractions for 430/920, 725/610 is 5/56120.