Use our free GCF of Fractions Calculator tool to compute the GCF of 328/258, 300/414 i.e 4/17802 easily. The following is the detailed procedure to determine the greatest common factor of fractions 328/258, 300/414.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 328/258,300/414
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 328/258,300/414, numerators are 328,300
Denominators are 258,414
The GCF of 328,300 is 4 .
LCM of 258,414 is 17802.
The greatest common factor of 328/258,300/414 = [GCF of 328,300]/[LCM of 258,414]= 4/17802
Therefore, the GCF of 328/258,300/414 is 4/17802.
To find the highest common factor of 328,300, we have to find the factors of both numbers and list the highest common factor.
The factors of 328 are 1, 2, 4, 8, 41, 82, 164, 328
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
The HCF of 328,300 is 4.
Lets's calculate GCF of 328,300
2 | 328, 300 |
2 | 164, 150 |
82, 75 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 328
:1,2,4,8,41,82,164,328
Now, list down the factors of 300
:1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300
Greatest Common Factor
We found the factors 328,300 . The biggest common factor number is the GCF number.
So the greatest common factor 328,300 is 4.
Lets's calculate LCM of 258,414
2 | 258, 414 |
3 | 129, 207 |
43, 69 |
∴ So the LCM of the given numbers is 2 x 3 x 43 x 69 = 17802
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/17802
Therefore, the GCF of Fractions 328/258,300/414 is 4/17802
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 258,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(258,414) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(258,414) x common factors =6 x 1 = 6
LCM(258,414) = ( 258 × 414 ) / 6
LCM(258,414) = 106812 / 6
LCM(258,414) = 17802
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 328,300?
The HCF of 328,300 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 328/258, 300/414?
Answer: GCF of Numerators as per given numbers 328/258, 300/414 is
GCF of Numerators i.e. for 328,300 is 4
LCM of denominators i.e. for 258,414 is 17802.
Thus, GCF of Fractions is 4/17802.Finally, GCF of Fractions for 328/258, 300/414 is 4/17802.