Use our free GCF of Fractions Calculator tool to compute the GCF of 32/312, 2193/7422 i.e 1/385944 easily. The following is the detailed procedure to determine the greatest common factor of fractions 32/312, 2193/7422.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 32/312,2193/7422
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 32/312,2193/7422, numerators are 32,2193
Denominators are 312,7422
The GCF of 32,2193 is 1 .
LCM of 312,7422 is 385944.
The greatest common factor of 32/312,2193/7422 = [GCF of 32,2193]/[LCM of 312,7422]= 1/385944
Therefore, the GCF of 32/312,2193/7422 is 1/385944.
To find the highest common factor of 32,2193, we have to find the factors of both numbers and list the highest common factor.
The factors of 32 are 1, 2, 4, 8, 16, 32
The factors of 2193 are 1, 3, 17, 43, 51, 129, 731, 2193
The HCF of 32,2193 is 1.
Lets's calculate GCF of 32,2193
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 32
:1,2,4,8,16,32
Now, list down the factors of 2193
:1,3,17,43,51,129,731,2193
Greatest Common Factor
We found the factors 32,2193 . The biggest common factor number is the GCF number.
So the greatest common factor 32,2193 is 1.
Lets's calculate LCM of 312,7422
2 | 312, 7422 |
3 | 156, 3711 |
52, 1237 |
∴ So the LCM of the given numbers is 2 x 3 x 52 x 1237 = 385944
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/385944
Therefore, the GCF of Fractions 32/312,2193/7422 is 1/385944
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 312,7422 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,7422) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(312,7422) x common factors =6 x 1 = 6
LCM(312,7422) = ( 312 × 7422 ) / 6
LCM(312,7422) = 2315664 / 6
LCM(312,7422) = 385944
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 32,2193?
The HCF of 32,2193 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 32/312, 2193/7422?
Answer: GCF of Numerators as per given numbers 32/312, 2193/7422 is
GCF of Numerators i.e. for 32,2193 is 1
LCM of denominators i.e. for 312,7422 is 385944.
Thus, GCF of Fractions is 1/385944.Finally, GCF of Fractions for 32/312, 2193/7422 is 1/385944.