Use our free GCF of Fractions Calculator tool to compute the GCF of 497/584, 966/456 i.e 7/33288 easily. The following is the detailed procedure to determine the greatest common factor of fractions 497/584, 966/456.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 497/584,966/456
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 497/584,966/456, numerators are 497,966
Denominators are 584,456
The GCF of 497,966 is 7 .
LCM of 584,456 is 33288.
The greatest common factor of 497/584,966/456 = [GCF of 497,966]/[LCM of 584,456]= 7/33288
Therefore, the GCF of 497/584,966/456 is 7/33288.
To find the highest common factor of 497,966, we have to find the factors of both numbers and list the highest common factor.
The factors of 497 are 1, 7, 71, 497
The factors of 966 are 1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966
The HCF of 497,966 is 7.
Lets's calculate GCF of 497,966
7 | 497, 966 |
71, 138 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 497
:1,7,71,497
Now, list down the factors of 966
:1,2,3,6,7,14,21,23,42,46,69,138,161,322,483,966
Greatest Common Factor
We found the factors 497,966 . The biggest common factor number is the GCF number.
So the greatest common factor 497,966 is 7.
Lets's calculate LCM of 584,456
2 | 584, 456 |
2 | 292, 228 |
2 | 146, 114 |
73, 57 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 73 x 57 = 33288
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/33288
Therefore, the GCF of Fractions 497/584,966/456 is 7/33288
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 584,456 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(584,456) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(584,456) x common factors =8 x 1 = 8
LCM(584,456) = ( 584 × 456 ) / 8
LCM(584,456) = 266304 / 8
LCM(584,456) = 33288
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 497,966?
The HCF of 497,966 is 7
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 497/584, 966/456?
Answer: GCF of Numerators as per given numbers 497/584, 966/456 is
GCF of Numerators i.e. for 497,966 is 7
LCM of denominators i.e. for 584,456 is 33288.
Thus, GCF of Fractions is 7/33288.Finally, GCF of Fractions for 497/584, 966/456 is 7/33288.