Use our free GCF of Fractions Calculator tool to compute the GCF of 294/323, 628/408 i.e 2/7752 easily. The following is the detailed procedure to determine the greatest common factor of fractions 294/323, 628/408.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 294/323,628/408
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 294/323,628/408, numerators are 294,628
Denominators are 323,408
The GCF of 294,628 is 2 .
LCM of 323,408 is 7752.
The greatest common factor of 294/323,628/408 = [GCF of 294,628]/[LCM of 323,408]= 2/7752
Therefore, the GCF of 294/323,628/408 is 2/7752.
To find the highest common factor of 294,628, we have to find the factors of both numbers and list the highest common factor.
The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
The factors of 628 are 1, 2, 4, 157, 314, 628
The HCF of 294,628 is 2.
Lets's calculate GCF of 294,628
2 | 294, 628 |
147, 314 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 294
:1,2,3,6,7,14,21,42,49,98,147,294
Now, list down the factors of 628
:1,2,4,157,314,628
Greatest Common Factor
We found the factors 294,628 . The biggest common factor number is the GCF number.
So the greatest common factor 294,628 is 2.
Lets's calculate LCM of 323,408
17 | 323, 408 |
19, 24 |
∴ So the LCM of the given numbers is 17 x 19 x 24 = 7752
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/7752
Therefore, the GCF of Fractions 294/323,628/408 is 2/7752
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 323,408 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(323,408) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(323,408) x common factors =17 x 1 = 17
LCM(323,408) = ( 323 × 408 ) / 17
LCM(323,408) = 131784 / 17
LCM(323,408) = 7752
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 294,628?
The HCF of 294,628 is 2
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 294/323, 628/408?
Answer: GCF of Numerators as per given numbers 294/323, 628/408 is
GCF of Numerators i.e. for 294,628 is 2
LCM of denominators i.e. for 323,408 is 7752.
Thus, GCF of Fractions is 2/7752.Finally, GCF of Fractions for 294/323, 628/408 is 2/7752.