Use our free GCF of Fractions Calculator tool to compute the GCF of 205/154, 774/802 i.e 1/61754 easily. The following is the detailed procedure to determine the greatest common factor of fractions 205/154, 774/802.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 205/154,774/802
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 205/154,774/802, numerators are 205,774
Denominators are 154,802
The GCF of 205,774 is 1 .
LCM of 154,802 is 61754.
The greatest common factor of 205/154,774/802 = [GCF of 205,774]/[LCM of 154,802]= 1/61754
Therefore, the GCF of 205/154,774/802 is 1/61754.
To find the highest common factor of 205,774, 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 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774
The HCF of 205,774 is 1.
Lets's calculate GCF of 205,774
∴ 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 774
:1,2,3,6,9,18,43,86,129,258,387,774
Greatest Common Factor
We found the factors 205,774 . The biggest common factor number is the GCF number.
So the greatest common factor 205,774 is 1.
Lets's calculate LCM of 154,802
2 | 154, 802 |
77, 401 |
∴ So the LCM of the given numbers is 2 x 77 x 401 = 61754
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/61754
Therefore, the GCF of Fractions 205/154,774/802 is 1/61754
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 154,802 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(154,802) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(154,802) x common factors =2 x 1 = 2
LCM(154,802) = ( 154 × 802 ) / 2
LCM(154,802) = 123508 / 2
LCM(154,802) = 61754
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 205,774?
The HCF of 205,774 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 205/154, 774/802?
Answer: GCF of Numerators as per given numbers 205/154, 774/802 is
GCF of Numerators i.e. for 205,774 is 1
LCM of denominators i.e. for 154,802 is 61754.
Thus, GCF of Fractions is 1/61754.Finally, GCF of Fractions for 205/154, 774/802 is 1/61754.