Use our free GCF of Fractions Calculator tool to compute the GCF of 465/309, 4914/9819 i.e 3/1011357 easily. The following is the detailed procedure to determine the greatest common factor of fractions 465/309, 4914/9819.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 465/309,4914/9819
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 465/309,4914/9819, numerators are 465,4914
Denominators are 309,9819
The GCF of 465,4914 is 3 .
LCM of 309,9819 is 1011357.
The greatest common factor of 465/309,4914/9819 = [GCF of 465,4914]/[LCM of 309,9819]= 3/1011357
Therefore, the GCF of 465/309,4914/9819 is 3/1011357.
To find the highest common factor of 465,4914, we have to find the factors of both numbers and list the highest common factor.
The factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465
The factors of 4914 are 1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 27, 39, 42, 54, 63, 78, 91, 117, 126, 182, 189, 234, 273, 351, 378, 546, 702, 819, 1638, 2457, 4914
The HCF of 465,4914 is 3.
Lets's calculate GCF of 465,4914
3 | 465, 4914 |
155, 1638 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 465
:1,3,5,15,31,93,155,465
Now, list down the factors of 4914
:1,2,3,6,7,9,13,14,18,21,26,27,39,42,54,63,78,91,117,126,182,189,234,273,351,378,546,702,819,1638,2457,4914
Greatest Common Factor
We found the factors 465,4914 . The biggest common factor number is the GCF number.
So the greatest common factor 465,4914 is 3.
Lets's calculate LCM of 309,9819
3 | 309, 9819 |
103, 3273 |
∴ So the LCM of the given numbers is 3 x 103 x 3273 = 1011357
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1011357
Therefore, the GCF of Fractions 465/309,4914/9819 is 3/1011357
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 309,9819 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,9819) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(309,9819) x common factors =3 x 1 = 3
LCM(309,9819) = ( 309 × 9819 ) / 3
LCM(309,9819) = 3034071 / 3
LCM(309,9819) = 1011357
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 465,4914?
The HCF of 465,4914 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 465/309, 4914/9819?
Answer: GCF of Numerators as per given numbers 465/309, 4914/9819 is
GCF of Numerators i.e. for 465,4914 is 3
LCM of denominators i.e. for 309,9819 is 1011357.
Thus, GCF of Fractions is 3/1011357.Finally, GCF of Fractions for 465/309, 4914/9819 is 3/1011357.