Use our free GCF of Fractions Calculator tool to compute the GCF of 2272/365, 6704/915 i.e 16/66795 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2272/365, 6704/915.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 2272/365,6704/915
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 2272/365,6704/915, numerators are 2272,6704
Denominators are 365,915
The GCF of 2272,6704 is 16 .
LCM of 365,915 is 66795.
The greatest common factor of 2272/365,6704/915 = [GCF of 2272,6704]/[LCM of 365,915]= 16/66795
Therefore, the GCF of 2272/365,6704/915 is 16/66795.
To find the highest common factor of 2272,6704, we have to find the factors of both numbers and list the highest common factor.
The factors of 2272 are 1, 2, 4, 8, 16, 32, 71, 142, 284, 568, 1136, 2272
The factors of 6704 are 1, 2, 4, 8, 16, 419, 838, 1676, 3352, 6704
The HCF of 2272,6704 is 16.
Lets's calculate GCF of 2272,6704
2 | 2272, 6704 |
2 | 1136, 3352 |
2 | 568, 1676 |
2 | 284, 838 |
142, 419 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Now, list down the factors of 2272
:1,2,4,8,16,32,71,142,284,568,1136,2272
Now, list down the factors of 6704
:1,2,4,8,16,419,838,1676,3352,6704
Greatest Common Factor
We found the factors 2272,6704 . The biggest common factor number is the GCF number.
So the greatest common factor 2272,6704 is 16.
Lets's calculate LCM of 365,915
5 | 365, 915 |
73, 183 |
∴ So the LCM of the given numbers is 5 x 73 x 183 = 66795
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/66795
Therefore, the GCF of Fractions 2272/365,6704/915 is 16/66795
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 365,915 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(365,915) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(365,915) x common factors =5 x 1 = 5
LCM(365,915) = ( 365 × 915 ) / 5
LCM(365,915) = 333975 / 5
LCM(365,915) = 66795
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 2272,6704?
The HCF of 2272,6704 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 2272/365, 6704/915?
Answer: GCF of Numerators as per given numbers 2272/365, 6704/915 is
GCF of Numerators i.e. for 2272,6704 is 16
LCM of denominators i.e. for 365,915 is 66795.
Thus, GCF of Fractions is 16/66795.Finally, GCF of Fractions for 2272/365, 6704/915 is 16/66795.