Use our free GCF of Fractions Calculator tool to compute the GCF of 208/410, 507/935 i.e 13/76670 easily. The following is the detailed procedure to determine the greatest common factor of fractions 208/410, 507/935.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 208/410,507/935
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 208/410,507/935, numerators are 208,507
Denominators are 410,935
The GCF of 208,507 is 13 .
LCM of 410,935 is 76670.
The greatest common factor of 208/410,507/935 = [GCF of 208,507]/[LCM of 410,935]= 13/76670
Therefore, the GCF of 208/410,507/935 is 13/76670.
To find the highest common factor of 208,507, we have to find the factors of both numbers and list the highest common factor.
The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
The factors of 507 are 1, 3, 13, 39, 169, 507
The HCF of 208,507 is 13.
Lets's calculate GCF of 208,507
13 | 208, 507 |
16, 39 |
∴ So the GCF of the given numbers is 13 = 13
Now, list down the factors of 208
:1,2,4,8,13,16,26,52,104,208
Now, list down the factors of 507
:1,3,13,39,169,507
Greatest Common Factor
We found the factors 208,507 . The biggest common factor number is the GCF number.
So the greatest common factor 208,507 is 13.
Lets's calculate LCM of 410,935
5 | 410, 935 |
82, 187 |
∴ So the LCM of the given numbers is 5 x 82 x 187 = 76670
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/76670
Therefore, the GCF of Fractions 208/410,507/935 is 13/76670
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 410,935 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(410,935) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(410,935) x common factors =5 x 1 = 5
LCM(410,935) = ( 410 × 935 ) / 5
LCM(410,935) = 383350 / 5
LCM(410,935) = 76670
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 208,507?
The HCF of 208,507 is 13
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 208/410, 507/935?
Answer: GCF of Numerators as per given numbers 208/410, 507/935 is
GCF of Numerators i.e. for 208,507 is 13
LCM of denominators i.e. for 410,935 is 76670.
Thus, GCF of Fractions is 13/76670.Finally, GCF of Fractions for 208/410, 507/935 is 13/76670.