Use our free GCF of Fractions Calculator tool to compute the GCF of 205/224, 704/133 i.e 1/4256 easily. The following is the detailed procedure to determine the greatest common factor of fractions 205/224, 704/133.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 205/224,704/133
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 205/224,704/133, numerators are 205,704
Denominators are 224,133
The GCF of 205,704 is 1 .
LCM of 224,133 is 4256.
The greatest common factor of 205/224,704/133 = [GCF of 205,704]/[LCM of 224,133]= 1/4256
Therefore, the GCF of 205/224,704/133 is 1/4256.
To find the highest common factor of 205,704, we have to find the factors of both numbers and list the highest common factor.
The factors of 205 are 1, 5, 41, 205
The factors of 704 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704
The HCF of 205,704 is 1.
Lets's calculate GCF of 205,704
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 205
:1,5,41,205
Now, list down the factors of 704
:1,2,4,8,11,16,22,32,44,64,88,176,352,704
Greatest Common Factor
We found the factors 205,704 . The biggest common factor number is the GCF number.
So the greatest common factor 205,704 is 1.
Lets's calculate LCM of 224,133
7 | 224, 133 |
32, 19 |
∴ So the LCM of the given numbers is 7 x 32 x 19 = 4256
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4256
Therefore, the GCF of Fractions 205/224,704/133 is 1/4256
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 224,133 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(224,133) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(224,133) x common factors =7 x 1 = 7
LCM(224,133) = ( 224 × 133 ) / 7
LCM(224,133) = 29792 / 7
LCM(224,133) = 4256
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 205,704?
The HCF of 205,704 is 1
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 205/224, 704/133?
Answer: GCF of Numerators as per given numbers 205/224, 704/133 is
GCF of Numerators i.e. for 205,704 is 1
LCM of denominators i.e. for 224,133 is 4256.
Thus, GCF of Fractions is 1/4256.Finally, GCF of Fractions for 205/224, 704/133 is 1/4256.