Use our free GCF of Fractions Calculator tool to compute the GCF of 459/589, 208/651 i.e 1/12369 easily. The following is the detailed procedure to determine the greatest common factor of fractions 459/589, 208/651.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 459/589,208/651
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 459/589,208/651, numerators are 459,208
Denominators are 589,651
The GCF of 459,208 is 1 .
LCM of 589,651 is 12369.
The greatest common factor of 459/589,208/651 = [GCF of 459,208]/[LCM of 589,651]= 1/12369
Therefore, the GCF of 459/589,208/651 is 1/12369.
To find the highest common factor of 459,208, we have to find the factors of both numbers and list the highest common factor.
The factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459
The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
The HCF of 459,208 is 1.
Lets's calculate GCF of 459,208
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 459
:1,3,9,17,27,51,153,459
Now, list down the factors of 208
:1,2,4,8,13,16,26,52,104,208
Greatest Common Factor
We found the factors 459,208 . The biggest common factor number is the GCF number.
So the greatest common factor 459,208 is 1.
Lets's calculate LCM of 589,651
31 | 589, 651 |
19, 21 |
∴ So the LCM of the given numbers is 31 x 19 x 21 = 12369
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12369
Therefore, the GCF of Fractions 459/589,208/651 is 1/12369
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 589,651 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(589,651) = 31
common factors(in case of two or more numbers have common factors) = 1
GCF(589,651) x common factors =31 x 1 = 31
LCM(589,651) = ( 589 × 651 ) / 31
LCM(589,651) = 383439 / 31
LCM(589,651) = 12369
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 459,208?
The HCF of 459,208 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 459/589, 208/651?
Answer: GCF of Numerators as per given numbers 459/589, 208/651 is
GCF of Numerators i.e. for 459,208 is 1
LCM of denominators i.e. for 589,651 is 12369.
Thus, GCF of Fractions is 1/12369.Finally, GCF of Fractions for 459/589, 208/651 is 1/12369.