Use our free GCF of Fractions Calculator tool to compute the GCF of 259/132, 819/676 i.e 7/22308 easily. The following is the detailed procedure to determine the greatest common factor of fractions 259/132, 819/676.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 259/132,819/676
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 259/132,819/676, numerators are 259,819
Denominators are 132,676
The GCF of 259,819 is 7 .
LCM of 132,676 is 22308.
The greatest common factor of 259/132,819/676 = [GCF of 259,819]/[LCM of 132,676]= 7/22308
Therefore, the GCF of 259/132,819/676 is 7/22308.
To find the highest common factor of 259,819, we have to find the factors of both numbers and list the highest common factor.
The factors of 259 are 1, 7, 37, 259
The factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819
The HCF of 259,819 is 7.
Lets's calculate GCF of 259,819
7 | 259, 819 |
37, 117 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 259
:1,7,37,259
Now, list down the factors of 819
:1,3,7,9,13,21,39,63,91,117,273,819
Greatest Common Factor
We found the factors 259,819 . The biggest common factor number is the GCF number.
So the greatest common factor 259,819 is 7.
Lets's calculate LCM of 132,676
2 | 132, 676 |
2 | 66, 338 |
33, 169 |
∴ So the LCM of the given numbers is 2 x 2 x 33 x 169 = 22308
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/22308
Therefore, the GCF of Fractions 259/132,819/676 is 7/22308
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 132,676 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(132,676) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(132,676) x common factors =4 x 1 = 4
LCM(132,676) = ( 132 × 676 ) / 4
LCM(132,676) = 89232 / 4
LCM(132,676) = 22308
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 259,819?
The HCF of 259,819 is 7
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 259/132, 819/676?
Answer: GCF of Numerators as per given numbers 259/132, 819/676 is
GCF of Numerators i.e. for 259,819 is 7
LCM of denominators i.e. for 132,676 is 22308.
Thus, GCF of Fractions is 7/22308.Finally, GCF of Fractions for 259/132, 819/676 is 7/22308.