Use our free GCF of Fractions Calculator tool to compute the GCF of 104/578, 735/916 i.e 1/264724 easily. The following is the detailed procedure to determine the greatest common factor of fractions 104/578, 735/916.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 104/578,735/916
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 104/578,735/916, numerators are 104,735
Denominators are 578,916
The GCF of 104,735 is 1 .
LCM of 578,916 is 264724.
The greatest common factor of 104/578,735/916 = [GCF of 104,735]/[LCM of 578,916]= 1/264724
Therefore, the GCF of 104/578,735/916 is 1/264724.
To find the highest common factor of 104,735, we have to find the factors of both numbers and list the highest common factor.
The factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104
The factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
The HCF of 104,735 is 1.
Lets's calculate GCF of 104,735
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 104
:1,2,4,8,13,26,52,104
Now, list down the factors of 735
:1,3,5,7,15,21,35,49,105,147,245,735
Greatest Common Factor
We found the factors 104,735 . The biggest common factor number is the GCF number.
So the greatest common factor 104,735 is 1.
Lets's calculate LCM of 578,916
2 | 578, 916 |
289, 458 |
∴ So the LCM of the given numbers is 2 x 289 x 458 = 264724
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/264724
Therefore, the GCF of Fractions 104/578,735/916 is 1/264724
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 578,916 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(578,916) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(578,916) x common factors =2 x 1 = 2
LCM(578,916) = ( 578 × 916 ) / 2
LCM(578,916) = 529448 / 2
LCM(578,916) = 264724
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 104,735?
The HCF of 104,735 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 104/578, 735/916?
Answer: GCF of Numerators as per given numbers 104/578, 735/916 is
GCF of Numerators i.e. for 104,735 is 1
LCM of denominators i.e. for 578,916 is 264724.
Thus, GCF of Fractions is 1/264724.Finally, GCF of Fractions for 104/578, 735/916 is 1/264724.