Use our free GCF of Fractions Calculator tool to compute the GCF of 304/221, 504/257 i.e 8/56797 easily. The following is the detailed procedure to determine the greatest common factor of fractions 304/221, 504/257.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 304/221,504/257
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 304/221,504/257, numerators are 304,504
Denominators are 221,257
The GCF of 304,504 is 8 .
LCM of 221,257 is 56797.
The greatest common factor of 304/221,504/257 = [GCF of 304,504]/[LCM of 221,257]= 8/56797
Therefore, the GCF of 304/221,504/257 is 8/56797.
To find the highest common factor of 304,504, we have to find the factors of both numbers and list the highest common factor.
The factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304
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 304,504 is 8.
Lets's calculate GCF of 304,504
2 | 304, 504 |
2 | 152, 252 |
2 | 76, 126 |
38, 63 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 304
:1,2,4,8,16,19,38,76,152,304
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 304,504 . The biggest common factor number is the GCF number.
So the greatest common factor 304,504 is 8.
Lets's calculate LCM of 221,257
Given numbers has no common factors except 1. So, there LCM is their product i.e 56797
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/56797
Therefore, the GCF of Fractions 304/221,504/257 is 8/56797
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 221,257 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(221,257) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(221,257) x common factors =1 x 1 = 1
LCM(221,257) = ( 221 × 257 ) / 1
LCM(221,257) = 56797 / 1
LCM(221,257) = 56797
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 304,504?
The HCF of 304,504 is 8
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 304/221, 504/257?
Answer: GCF of Numerators as per given numbers 304/221, 504/257 is
GCF of Numerators i.e. for 304,504 is 8
LCM of denominators i.e. for 221,257 is 56797.
Thus, GCF of Fractions is 8/56797.Finally, GCF of Fractions for 304/221, 504/257 is 8/56797.