Use our free GCF of Fractions Calculator tool to compute the GCF of 574/144, 413/482 i.e 7/34704 easily. The following is the detailed procedure to determine the greatest common factor of fractions 574/144, 413/482.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 574/144,413/482
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 574/144,413/482, numerators are 574,413
Denominators are 144,482
The GCF of 574,413 is 7 .
LCM of 144,482 is 34704.
The greatest common factor of 574/144,413/482 = [GCF of 574,413]/[LCM of 144,482]= 7/34704
Therefore, the GCF of 574/144,413/482 is 7/34704.
To find the highest common factor of 574,413, we have to find the factors of both numbers and list the highest common factor.
The factors of 574 are 1, 2, 7, 14, 41, 82, 287, 574
The factors of 413 are 1, 7, 59, 413
The HCF of 574,413 is 7.
Lets's calculate GCF of 574,413
7 | 574, 413 |
82, 59 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 574
:1,2,7,14,41,82,287,574
Now, list down the factors of 413
:1,7,59,413
Greatest Common Factor
We found the factors 574,413 . The biggest common factor number is the GCF number.
So the greatest common factor 574,413 is 7.
Lets's calculate LCM of 144,482
2 | 144, 482 |
72, 241 |
∴ So the LCM of the given numbers is 2 x 72 x 241 = 34704
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/34704
Therefore, the GCF of Fractions 574/144,413/482 is 7/34704
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 144,482 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(144,482) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(144,482) x common factors =2 x 1 = 2
LCM(144,482) = ( 144 × 482 ) / 2
LCM(144,482) = 69408 / 2
LCM(144,482) = 34704
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 574,413?
The HCF of 574,413 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 574/144, 413/482?
Answer: GCF of Numerators as per given numbers 574/144, 413/482 is
GCF of Numerators i.e. for 574,413 is 7
LCM of denominators i.e. for 144,482 is 34704.
Thus, GCF of Fractions is 7/34704.Finally, GCF of Fractions for 574/144, 413/482 is 7/34704.