Use our free GCF of Fractions Calculator tool to compute the GCF of 5584/193, 7216/6896 i.e 16/1330928 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5584/193, 7216/6896.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 5584/193,7216/6896
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 5584/193,7216/6896, numerators are 5584,7216
Denominators are 193,6896
The GCF of 5584,7216 is 16 .
LCM of 193,6896 is 1330928.
The greatest common factor of 5584/193,7216/6896 = [GCF of 5584,7216]/[LCM of 193,6896]= 16/1330928
Therefore, the GCF of 5584/193,7216/6896 is 16/1330928.
To find the highest common factor of 5584,7216, we have to find the factors of both numbers and list the highest common factor.
The factors of 5584 are 1, 2, 4, 8, 16, 349, 698, 1396, 2792, 5584
The factors of 7216 are 1, 2, 4, 8, 11, 16, 22, 41, 44, 82, 88, 164, 176, 328, 451, 656, 902, 1804, 3608, 7216
The HCF of 5584,7216 is 16.
Lets's calculate GCF of 5584,7216
2 | 5584, 7216 |
2 | 2792, 3608 |
2 | 1396, 1804 |
2 | 698, 902 |
349, 451 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Now, list down the factors of 5584
:1,2,4,8,16,349,698,1396,2792,5584
Now, list down the factors of 7216
:1,2,4,8,11,16,22,41,44,82,88,164,176,328,451,656,902,1804,3608,7216
Greatest Common Factor
We found the factors 5584,7216 . The biggest common factor number is the GCF number.
So the greatest common factor 5584,7216 is 16.
Lets's calculate LCM of 193,6896
Given numbers has no common factors except 1. So, there LCM is their product i.e 1330928
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/1330928
Therefore, the GCF of Fractions 5584/193,7216/6896 is 16/1330928
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 193,6896 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(193,6896) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(193,6896) x common factors =1 x 1 = 1
LCM(193,6896) = ( 193 × 6896 ) / 1
LCM(193,6896) = 1330928 / 1
LCM(193,6896) = 1330928
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 5584,7216?
The HCF of 5584,7216 is 16
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 5584/193, 7216/6896?
Answer: GCF of Numerators as per given numbers 5584/193, 7216/6896 is
GCF of Numerators i.e. for 5584,7216 is 16
LCM of denominators i.e. for 193,6896 is 1330928.
Thus, GCF of Fractions is 16/1330928.Finally, GCF of Fractions for 5584/193, 7216/6896 is 16/1330928.