Use our free GCF of Fractions Calculator tool to compute the GCF of 30/346, 75/996, 712/324 i.e 1/4652316 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/346, 75/996, 712/324.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 30/346,75/996,712/324
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 30/346,75/996,712/324, numerators are 30,75,712
Denominators are 346,996,324
The GCF of 30,75,712 is 1 .
LCM of 346,996,324 is 4652316.
The greatest common factor of 30/346,75/996,712/324 = [GCF of 30,75,712]/[LCM of 346,996,324]= 1/4652316
Therefore, the GCF of 30/346,75/996,712/324 is 1/4652316.
To find the highest common factor of 30,75,712, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 712 are 1, 2, 4, 8, 89, 178, 356, 712
The HCF of 30,75,712 is 1.
Lets's calculate GCF of 30,75,712
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 712
:1,2,4,8,89,178,356,712
Greatest Common Factor
We found the factors 30,75,712 . The biggest common factor number is the GCF number.
So the greatest common factor 30,75,712 is 1.
Lets's calculate LCM of 346,996,324
2 | 346, 996, 324 |
2 | 173, 498, 162 |
3 | 173, 249, 81 |
173, 83, 27 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 173 x 83 x 27 = 4652316
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4652316
Therefore, the GCF of Fractions 30/346,75/996,712/324 is 1/4652316
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 346,996,324 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(346,996,324) = 2
common factors(in case of two or more numbers have common factors) = 12
GCF(346,996,324) x common factors =2 x 12 = 24
LCM(346,996,324) = ( 346 × 996 × 324 ) / 24
LCM(346,996,324) = 111655584 / 24
LCM(346,996,324) = 4652316
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 30,75,712?
The HCF of 30,75,712 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 30/346, 75/996, 712/324?
Answer: GCF of Numerators as per given numbers 30/346, 75/996, 712/324 is
GCF of Numerators i.e. for 30,75,712 is 1
LCM of denominators i.e. for 346,996,324 is 4652316.
Thus, GCF of Fractions is 1/4652316.Finally, GCF of Fractions for 30/346, 75/996, 712/324 is 1/4652316.