Use our free GCF of Fractions Calculator tool to compute the GCF of 459/454, 578/504 i.e 17/114408 easily. The following is the detailed procedure to determine the greatest common factor of fractions 459/454, 578/504.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 459/454,578/504
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 459/454,578/504, numerators are 459,578
Denominators are 454,504
The GCF of 459,578 is 17 .
LCM of 454,504 is 114408.
The greatest common factor of 459/454,578/504 = [GCF of 459,578]/[LCM of 454,504]= 17/114408
Therefore, the GCF of 459/454,578/504 is 17/114408.
To find the highest common factor of 459,578, 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 578 are 1, 2, 17, 34, 289, 578
The HCF of 459,578 is 17.
Lets's calculate GCF of 459,578
17 | 459, 578 |
27, 34 |
∴ So the GCF of the given numbers is 17 = 17
Now, list down the factors of 459
:1,3,9,17,27,51,153,459
Now, list down the factors of 578
:1,2,17,34,289,578
Greatest Common Factor
We found the factors 459,578 . The biggest common factor number is the GCF number.
So the greatest common factor 459,578 is 17.
Lets's calculate LCM of 454,504
2 | 454, 504 |
227, 252 |
∴ So the LCM of the given numbers is 2 x 227 x 252 = 114408
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/114408
Therefore, the GCF of Fractions 459/454,578/504 is 17/114408
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 454,504 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(454,504) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(454,504) x common factors =2 x 1 = 2
LCM(454,504) = ( 454 × 504 ) / 2
LCM(454,504) = 228816 / 2
LCM(454,504) = 114408
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 459,578?
The HCF of 459,578 is 17
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 459/454, 578/504?
Answer: GCF of Numerators as per given numbers 459/454, 578/504 is
GCF of Numerators i.e. for 459,578 is 17
LCM of denominators i.e. for 454,504 is 114408.
Thus, GCF of Fractions is 17/114408.Finally, GCF of Fractions for 459/454, 578/504 is 17/114408.