Use our free GCF of Fractions Calculator tool to compute the GCF of 396/448, 520/413 i.e 4/26432 easily. The following is the detailed procedure to determine the greatest common factor of fractions 396/448, 520/413.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 396/448,520/413
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 396/448,520/413, numerators are 396,520
Denominators are 448,413
The GCF of 396,520 is 4 .
LCM of 448,413 is 26432.
The greatest common factor of 396/448,520/413 = [GCF of 396,520]/[LCM of 448,413]= 4/26432
Therefore, the GCF of 396/448,520/413 is 4/26432.
To find the highest common factor of 396,520, we have to find the factors of both numbers and list the highest common factor.
The factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396
The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520
The HCF of 396,520 is 4.
Lets's calculate GCF of 396,520
2 | 396, 520 |
2 | 198, 260 |
99, 130 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 396
:1,2,3,4,6,9,11,12,18,22,33,36,44,66,99,132,198,396
Now, list down the factors of 520
:1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520
Greatest Common Factor
We found the factors 396,520 . The biggest common factor number is the GCF number.
So the greatest common factor 396,520 is 4.
Lets's calculate LCM of 448,413
7 | 448, 413 |
64, 59 |
∴ So the LCM of the given numbers is 7 x 64 x 59 = 26432
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/26432
Therefore, the GCF of Fractions 396/448,520/413 is 4/26432
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 448,413 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(448,413) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(448,413) x common factors =7 x 1 = 7
LCM(448,413) = ( 448 × 413 ) / 7
LCM(448,413) = 185024 / 7
LCM(448,413) = 26432
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 396,520?
The HCF of 396,520 is 4
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 396/448, 520/413?
Answer: GCF of Numerators as per given numbers 396/448, 520/413 is
GCF of Numerators i.e. for 396,520 is 4
LCM of denominators i.e. for 448,413 is 26432.
Thus, GCF of Fractions is 4/26432.Finally, GCF of Fractions for 396/448, 520/413 is 4/26432.