Use our free GCF of Fractions Calculator tool to compute the GCF of 825/735, 342/591 i.e 3/144795 easily. The following is the detailed procedure to determine the greatest common factor of fractions 825/735, 342/591.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 825/735,342/591
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 825/735,342/591, numerators are 825,342
Denominators are 735,591
The GCF of 825,342 is 3 .
LCM of 735,591 is 144795.
The greatest common factor of 825/735,342/591 = [GCF of 825,342]/[LCM of 735,591]= 3/144795
Therefore, the GCF of 825/735,342/591 is 3/144795.
To find the highest common factor of 825,342, we have to find the factors of both numbers and list the highest common factor.
The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The HCF of 825,342 is 3.
Lets's calculate GCF of 825,342
3 | 825, 342 |
275, 114 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 825
:1,3,5,11,15,25,33,55,75,165,275,825
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Greatest Common Factor
We found the factors 825,342 . The biggest common factor number is the GCF number.
So the greatest common factor 825,342 is 3.
Lets's calculate LCM of 735,591
3 | 735, 591 |
245, 197 |
∴ So the LCM of the given numbers is 3 x 245 x 197 = 144795
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/144795
Therefore, the GCF of Fractions 825/735,342/591 is 3/144795
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 735,591 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(735,591) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(735,591) x common factors =3 x 1 = 3
LCM(735,591) = ( 735 × 591 ) / 3
LCM(735,591) = 434385 / 3
LCM(735,591) = 144795
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 825,342?
The HCF of 825,342 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 825/735, 342/591?
Answer: GCF of Numerators as per given numbers 825/735, 342/591 is
GCF of Numerators i.e. for 825,342 is 3
LCM of denominators i.e. for 735,591 is 144795.
Thus, GCF of Fractions is 3/144795.Finally, GCF of Fractions for 825/735, 342/591 is 3/144795.