Use our free GCF of Fractions Calculator tool to compute the GCF of 327/36, 612/964 i.e 3/8676 easily. The following is the detailed procedure to determine the greatest common factor of fractions 327/36, 612/964.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 327/36,612/964
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 327/36,612/964, numerators are 327,612
Denominators are 36,964
The GCF of 327,612 is 3 .
LCM of 36,964 is 8676.
The greatest common factor of 327/36,612/964 = [GCF of 327,612]/[LCM of 36,964]= 3/8676
Therefore, the GCF of 327/36,612/964 is 3/8676.
To find the highest common factor of 327,612, we have to find the factors of both numbers and list the highest common factor.
The factors of 327 are 1, 3, 109, 327
The factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612
The HCF of 327,612 is 3.
Lets's calculate GCF of 327,612
3 | 327, 612 |
109, 204 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 327
:1,3,109,327
Now, list down the factors of 612
:1,2,3,4,6,9,12,17,18,34,36,51,68,102,153,204,306,612
Greatest Common Factor
We found the factors 327,612 . The biggest common factor number is the GCF number.
So the greatest common factor 327,612 is 3.
Lets's calculate LCM of 36,964
2 | 36, 964 |
2 | 18, 482 |
9, 241 |
∴ So the LCM of the given numbers is 2 x 2 x 9 x 241 = 8676
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/8676
Therefore, the GCF of Fractions 327/36,612/964 is 3/8676
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 36,964 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(36,964) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(36,964) x common factors =4 x 1 = 4
LCM(36,964) = ( 36 × 964 ) / 4
LCM(36,964) = 34704 / 4
LCM(36,964) = 8676
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 327,612?
The HCF of 327,612 is 3
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 327/36, 612/964?
Answer: GCF of Numerators as per given numbers 327/36, 612/964 is
GCF of Numerators i.e. for 327,612 is 3
LCM of denominators i.e. for 36,964 is 8676.
Thus, GCF of Fractions is 3/8676.Finally, GCF of Fractions for 327/36, 612/964 is 3/8676.