Use our free GCF of Fractions Calculator tool to compute the GCF of 323/54, 350/784 i.e 1/21168 easily. The following is the detailed procedure to determine the greatest common factor of fractions 323/54, 350/784.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 323/54,350/784
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 323/54,350/784, numerators are 323,350
Denominators are 54,784
The GCF of 323,350 is 1 .
LCM of 54,784 is 21168.
The greatest common factor of 323/54,350/784 = [GCF of 323,350]/[LCM of 54,784]= 1/21168
Therefore, the GCF of 323/54,350/784 is 1/21168.
To find the highest common factor of 323,350, we have to find the factors of both numbers and list the highest common factor.
The factors of 323 are 1, 17, 19, 323
The factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350
The HCF of 323,350 is 1.
Lets's calculate GCF of 323,350
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 323
:1,17,19,323
Now, list down the factors of 350
:1,2,5,7,10,14,25,35,50,70,175,350
Greatest Common Factor
We found the factors 323,350 . The biggest common factor number is the GCF number.
So the greatest common factor 323,350 is 1.
Lets's calculate LCM of 54,784
2 | 54, 784 |
27, 392 |
∴ So the LCM of the given numbers is 2 x 27 x 392 = 21168
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/21168
Therefore, the GCF of Fractions 323/54,350/784 is 1/21168
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 54,784 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,784) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(54,784) x common factors =2 x 1 = 2
LCM(54,784) = ( 54 × 784 ) / 2
LCM(54,784) = 42336 / 2
LCM(54,784) = 21168
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 323,350?
The HCF of 323,350 is 1
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 323/54, 350/784?
Answer: GCF of Numerators as per given numbers 323/54, 350/784 is
GCF of Numerators i.e. for 323,350 is 1
LCM of denominators i.e. for 54,784 is 21168.
Thus, GCF of Fractions is 1/21168.Finally, GCF of Fractions for 323/54, 350/784 is 1/21168.