Use our free GCF of Fractions Calculator tool to compute the GCF of 531/396, 649/174 i.e 59/11484 easily. The following is the detailed procedure to determine the greatest common factor of fractions 531/396, 649/174.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 531/396,649/174
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 531/396,649/174, numerators are 531,649
Denominators are 396,174
The GCF of 531,649 is 59 .
LCM of 396,174 is 11484.
The greatest common factor of 531/396,649/174 = [GCF of 531,649]/[LCM of 396,174]= 59/11484
Therefore, the GCF of 531/396,649/174 is 59/11484.
To find the highest common factor of 531,649, we have to find the factors of both numbers and list the highest common factor.
The factors of 531 are 1, 3, 9, 59, 177, 531
The factors of 649 are 1, 11, 59, 649
The HCF of 531,649 is 59.
Lets's calculate GCF of 531,649
59 | 531, 649 |
9, 11 |
∴ So the GCF of the given numbers is 59 = 59
Now, list down the factors of 531
:1,3,9,59,177,531
Now, list down the factors of 649
:1,11,59,649
Greatest Common Factor
We found the factors 531,649 . The biggest common factor number is the GCF number.
So the greatest common factor 531,649 is 59.
Lets's calculate LCM of 396,174
2 | 396, 174 |
3 | 198, 87 |
66, 29 |
∴ So the LCM of the given numbers is 2 x 3 x 66 x 29 = 11484
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 59/11484
Therefore, the GCF of Fractions 531/396,649/174 is 59/11484
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 396,174 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(396,174) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(396,174) x common factors =6 x 1 = 6
LCM(396,174) = ( 396 × 174 ) / 6
LCM(396,174) = 68904 / 6
LCM(396,174) = 11484
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 531,649?
The HCF of 531,649 is 59
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 531/396, 649/174?
Answer: GCF of Numerators as per given numbers 531/396, 649/174 is
GCF of Numerators i.e. for 531,649 is 59
LCM of denominators i.e. for 396,174 is 11484.
Thus, GCF of Fractions is 59/11484.Finally, GCF of Fractions for 531/396, 649/174 is 59/11484.