Use our free GCF of Fractions Calculator tool to compute the GCF of 409/431, 842/653 i.e 1/281443 easily. The following is the detailed procedure to determine the greatest common factor of fractions 409/431, 842/653.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 409/431,842/653
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 409/431,842/653, numerators are 409,842
Denominators are 431,653
The GCF of 409,842 is 1 .
LCM of 431,653 is 281443.
The greatest common factor of 409/431,842/653 = [GCF of 409,842]/[LCM of 431,653]= 1/281443
Therefore, the GCF of 409/431,842/653 is 1/281443.
To find the highest common factor of 409,842, we have to find the factors of both numbers and list the highest common factor.
The factors of 409 are 1, 409
The factors of 842 are 1, 2, 421, 842
The HCF of 409,842 is 1.
Lets's calculate GCF of 409,842
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 409
:1,409
Now, list down the factors of 842
:1,2,421,842
Greatest Common Factor
We found the factors 409,842 . The biggest common factor number is the GCF number.
So the greatest common factor 409,842 is 1.
Lets's calculate LCM of 431,653
Given numbers has no common factors except 1. So, there LCM is their product i.e 281443
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/281443
Therefore, the GCF of Fractions 409/431,842/653 is 1/281443
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 431,653 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(431,653) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(431,653) x common factors =1 x 1 = 1
LCM(431,653) = ( 431 × 653 ) / 1
LCM(431,653) = 281443 / 1
LCM(431,653) = 281443
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 409,842?
The HCF of 409,842 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 409/431, 842/653?
Answer: GCF of Numerators as per given numbers 409/431, 842/653 is
GCF of Numerators i.e. for 409,842 is 1
LCM of denominators i.e. for 431,653 is 281443.
Thus, GCF of Fractions is 1/281443.Finally, GCF of Fractions for 409/431, 842/653 is 1/281443.