Use our free GCF of Fractions Calculator tool to compute the GCF of 854/289, 157/731 i.e 1/12427 easily. The following is the detailed procedure to determine the greatest common factor of fractions 854/289, 157/731.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 854/289,157/731
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 854/289,157/731, numerators are 854,157
Denominators are 289,731
The GCF of 854,157 is 1 .
LCM of 289,731 is 12427.
The greatest common factor of 854/289,157/731 = [GCF of 854,157]/[LCM of 289,731]= 1/12427
Therefore, the GCF of 854/289,157/731 is 1/12427.
To find the highest common factor of 854,157, we have to find the factors of both numbers and list the highest common factor.
The factors of 854 are 1, 2, 7, 14, 61, 122, 427, 854
The factors of 157 are 1, 157
The HCF of 854,157 is 1.
Lets's calculate GCF of 854,157
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 854
:1,2,7,14,61,122,427,854
Now, list down the factors of 157
:1,157
Greatest Common Factor
We found the factors 854,157 . The biggest common factor number is the GCF number.
So the greatest common factor 854,157 is 1.
Lets's calculate LCM of 289,731
17 | 289, 731 |
17, 43 |
∴ So the LCM of the given numbers is 17 x 17 x 43 = 12427
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12427
Therefore, the GCF of Fractions 854/289,157/731 is 1/12427
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 289,731 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(289,731) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(289,731) x common factors =17 x 1 = 17
LCM(289,731) = ( 289 × 731 ) / 17
LCM(289,731) = 211259 / 17
LCM(289,731) = 12427
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 854,157?
The HCF of 854,157 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 854/289, 157/731?
Answer: GCF of Numerators as per given numbers 854/289, 157/731 is
GCF of Numerators i.e. for 854,157 is 1
LCM of denominators i.e. for 289,731 is 12427.
Thus, GCF of Fractions is 1/12427.Finally, GCF of Fractions for 854/289, 157/731 is 1/12427.