Use our free GCF of Fractions Calculator tool to compute the GCF of 643/571, 507/409 i.e 1/233539 easily. The following is the detailed procedure to determine the greatest common factor of fractions 643/571, 507/409.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 643/571,507/409
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 643/571,507/409, numerators are 643,507
Denominators are 571,409
The GCF of 643,507 is 1 .
LCM of 571,409 is 233539.
The greatest common factor of 643/571,507/409 = [GCF of 643,507]/[LCM of 571,409]= 1/233539
Therefore, the GCF of 643/571,507/409 is 1/233539.
To find the highest common factor of 643,507, we have to find the factors of both numbers and list the highest common factor.
The factors of 643 are 1, 643
The factors of 507 are 1, 3, 13, 39, 169, 507
The HCF of 643,507 is 1.
Lets's calculate GCF of 643,507
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 643
:1,643
Now, list down the factors of 507
:1,3,13,39,169,507
Greatest Common Factor
We found the factors 643,507 . The biggest common factor number is the GCF number.
So the greatest common factor 643,507 is 1.
Lets's calculate LCM of 571,409
Given numbers has no common factors except 1. So, there LCM is their product i.e 233539
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/233539
Therefore, the GCF of Fractions 643/571,507/409 is 1/233539
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 571,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(571,409) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(571,409) x common factors =1 x 1 = 1
LCM(571,409) = ( 571 × 409 ) / 1
LCM(571,409) = 233539 / 1
LCM(571,409) = 233539
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 643,507?
The HCF of 643,507 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 643/571, 507/409?
Answer: GCF of Numerators as per given numbers 643/571, 507/409 is
GCF of Numerators i.e. for 643,507 is 1
LCM of denominators i.e. for 571,409 is 233539.
Thus, GCF of Fractions is 1/233539.Finally, GCF of Fractions for 643/571, 507/409 is 1/233539.