Use our free GCF of Fractions Calculator tool to compute the GCF of 408/301, 504/539 i.e 24/23177 easily. The following is the detailed procedure to determine the greatest common factor of fractions 408/301, 504/539.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 408/301,504/539
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 408/301,504/539, numerators are 408,504
Denominators are 301,539
The GCF of 408,504 is 24 .
LCM of 301,539 is 23177.
The greatest common factor of 408/301,504/539 = [GCF of 408,504]/[LCM of 301,539]= 24/23177
Therefore, the GCF of 408/301,504/539 is 24/23177.
To find the highest common factor of 408,504, we have to find the factors of both numbers and list the highest common factor.
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
The HCF of 408,504 is 24.
Lets's calculate GCF of 408,504
2 | 408, 504 |
2 | 204, 252 |
2 | 102, 126 |
3 | 51, 63 |
17, 21 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Now, list down the factors of 504
:1,2,3,4,6,7,8,9,12,14,18,21,24,28,36,42,56,63,72,84,126,168,252,504
Greatest Common Factor
We found the factors 408,504 . The biggest common factor number is the GCF number.
So the greatest common factor 408,504 is 24.
Lets's calculate LCM of 301,539
7 | 301, 539 |
43, 77 |
∴ So the LCM of the given numbers is 7 x 43 x 77 = 23177
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/23177
Therefore, the GCF of Fractions 408/301,504/539 is 24/23177
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 301,539 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(301,539) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(301,539) x common factors =7 x 1 = 7
LCM(301,539) = ( 301 × 539 ) / 7
LCM(301,539) = 162239 / 7
LCM(301,539) = 23177
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 408,504?
The HCF of 408,504 is 24
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 408/301, 504/539?
Answer: GCF of Numerators as per given numbers 408/301, 504/539 is
GCF of Numerators i.e. for 408,504 is 24
LCM of denominators i.e. for 301,539 is 23177.
Thus, GCF of Fractions is 24/23177.Finally, GCF of Fractions for 408/301, 504/539 is 24/23177.