Use our free GCF of Fractions Calculator tool to compute the GCF of 321/382, 642/328 i.e 321/62648 easily. The following is the detailed procedure to determine the greatest common factor of fractions 321/382, 642/328.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 321/382,642/328
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 321/382,642/328, numerators are 321,642
Denominators are 382,328
The GCF of 321,642 is 321 .
LCM of 382,328 is 62648.
The greatest common factor of 321/382,642/328 = [GCF of 321,642]/[LCM of 382,328]= 321/62648
Therefore, the GCF of 321/382,642/328 is 321/62648.
To find the highest common factor of 321,642, we have to find the factors of both numbers and list the highest common factor.
The factors of 321 are 1, 3, 107, 321
The factors of 642 are 1, 2, 3, 6, 107, 214, 321, 642
The HCF of 321,642 is 321.
Lets's calculate GCF of 321,642
3 | 321, 642 |
107 | 107, 214 |
1, 2 |
∴ So the GCF of the given numbers is 3 x 107 = 321
Now, list down the factors of 321
:1,3,107,321
Now, list down the factors of 642
:1,2,3,6,107,214,321,642
Greatest Common Factor
We found the factors 321,642 . The biggest common factor number is the GCF number.
So the greatest common factor 321,642 is 321.
Lets's calculate LCM of 382,328
2 | 382, 328 |
191, 164 |
∴ So the LCM of the given numbers is 2 x 191 x 164 = 62648
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 321/62648
Therefore, the GCF of Fractions 321/382,642/328 is 321/62648
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 382,328 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(382,328) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(382,328) x common factors =2 x 1 = 2
LCM(382,328) = ( 382 × 328 ) / 2
LCM(382,328) = 125296 / 2
LCM(382,328) = 62648
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 321,642?
The HCF of 321,642 is 321
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 321/382, 642/328?
Answer: GCF of Numerators as per given numbers 321/382, 642/328 is
GCF of Numerators i.e. for 321,642 is 321
LCM of denominators i.e. for 382,328 is 62648.
Thus, GCF of Fractions is 321/62648.Finally, GCF of Fractions for 321/382, 642/328 is 321/62648.