Use our free GCF of Fractions Calculator tool to compute the GCF of 213/517, 507/990 i.e 3/46530 easily. The following is the detailed procedure to determine the greatest common factor of fractions 213/517, 507/990.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 213/517,507/990
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 213/517,507/990, numerators are 213,507
Denominators are 517,990
The GCF of 213,507 is 3 .
LCM of 517,990 is 46530.
The greatest common factor of 213/517,507/990 = [GCF of 213,507]/[LCM of 517,990]= 3/46530
Therefore, the GCF of 213/517,507/990 is 3/46530.
To find the highest common factor of 213,507, we have to find the factors of both numbers and list the highest common factor.
The factors of 213 are 1, 3, 71, 213
The factors of 507 are 1, 3, 13, 39, 169, 507
The HCF of 213,507 is 3.
Lets's calculate GCF of 213,507
3 | 213, 507 |
71, 169 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 213
:1,3,71,213
Now, list down the factors of 507
:1,3,13,39,169,507
Greatest Common Factor
We found the factors 213,507 . The biggest common factor number is the GCF number.
So the greatest common factor 213,507 is 3.
Lets's calculate LCM of 517,990
11 | 517, 990 |
47, 90 |
∴ So the LCM of the given numbers is 11 x 47 x 90 = 46530
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/46530
Therefore, the GCF of Fractions 213/517,507/990 is 3/46530
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 517,990 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(517,990) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(517,990) x common factors =11 x 1 = 11
LCM(517,990) = ( 517 × 990 ) / 11
LCM(517,990) = 511830 / 11
LCM(517,990) = 46530
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 213,507?
The HCF of 213,507 is 3
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 213/517, 507/990?
Answer: GCF of Numerators as per given numbers 213/517, 507/990 is
GCF of Numerators i.e. for 213,507 is 3
LCM of denominators i.e. for 517,990 is 46530.
Thus, GCF of Fractions is 3/46530.Finally, GCF of Fractions for 213/517, 507/990 is 3/46530.