Use our free GCF of Fractions Calculator tool to compute the GCF of 321/199, 493/560 i.e 1/111440 easily. The following is the detailed procedure to determine the greatest common factor of fractions 321/199, 493/560.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 321/199,493/560
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 321/199,493/560, numerators are 321,493
Denominators are 199,560
The GCF of 321,493 is 1 .
LCM of 199,560 is 111440.
The greatest common factor of 321/199,493/560 = [GCF of 321,493]/[LCM of 199,560]= 1/111440
Therefore, the GCF of 321/199,493/560 is 1/111440.
To find the highest common factor of 321,493, 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 493 are 1, 17, 29, 493
The HCF of 321,493 is 1.
Lets's calculate GCF of 321,493
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 321
:1,3,107,321
Now, list down the factors of 493
:1,17,29,493
Greatest Common Factor
We found the factors 321,493 . The biggest common factor number is the GCF number.
So the greatest common factor 321,493 is 1.
Lets's calculate LCM of 199,560
Given numbers has no common factors except 1. So, there LCM is their product i.e 111440
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/111440
Therefore, the GCF of Fractions 321/199,493/560 is 1/111440
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 199,560 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(199,560) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(199,560) x common factors =1 x 1 = 1
LCM(199,560) = ( 199 × 560 ) / 1
LCM(199,560) = 111440 / 1
LCM(199,560) = 111440
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 321,493?
The HCF of 321,493 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 321/199, 493/560?
Answer: GCF of Numerators as per given numbers 321/199, 493/560 is
GCF of Numerators i.e. for 321,493 is 1
LCM of denominators i.e. for 199,560 is 111440.
Thus, GCF of Fractions is 1/111440.Finally, GCF of Fractions for 321/199, 493/560 is 1/111440.