Use our free GCF of Fractions Calculator tool to compute the GCF of 759/21, 516/1904 i.e 3/5712 easily. The following is the detailed procedure to determine the greatest common factor of fractions 759/21, 516/1904.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 759/21,516/1904
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 759/21,516/1904, numerators are 759,516
Denominators are 21,1904
The GCF of 759,516 is 3 .
LCM of 21,1904 is 5712.
The greatest common factor of 759/21,516/1904 = [GCF of 759,516]/[LCM of 21,1904]= 3/5712
Therefore, the GCF of 759/21,516/1904 is 3/5712.
To find the highest common factor of 759,516, we have to find the factors of both numbers and list the highest common factor.
The factors of 759 are 1, 3, 11, 23, 33, 69, 253, 759
The factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516
The HCF of 759,516 is 3.
Lets's calculate GCF of 759,516
3 | 759, 516 |
253, 172 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 759
:1,3,11,23,33,69,253,759
Now, list down the factors of 516
:1,2,3,4,6,12,43,86,129,172,258,516
Greatest Common Factor
We found the factors 759,516 . The biggest common factor number is the GCF number.
So the greatest common factor 759,516 is 3.
Lets's calculate LCM of 21,1904
7 | 21, 1904 |
3, 272 |
∴ So the LCM of the given numbers is 7 x 3 x 272 = 5712
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/5712
Therefore, the GCF of Fractions 759/21,516/1904 is 3/5712
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 21,1904 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,1904) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(21,1904) x common factors =7 x 1 = 7
LCM(21,1904) = ( 21 × 1904 ) / 7
LCM(21,1904) = 39984 / 7
LCM(21,1904) = 5712
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 759,516?
The HCF of 759,516 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 759/21, 516/1904?
Answer: GCF of Numerators as per given numbers 759/21, 516/1904 is
GCF of Numerators i.e. for 759,516 is 3
LCM of denominators i.e. for 21,1904 is 5712.
Thus, GCF of Fractions is 3/5712.Finally, GCF of Fractions for 759/21, 516/1904 is 3/5712.