Use our free GCF of Fractions Calculator tool to compute the GCF of 854/878, 469/561 i.e 7/492558 easily. The following is the detailed procedure to determine the greatest common factor of fractions 854/878, 469/561.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 854/878,469/561
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 854/878,469/561, numerators are 854,469
Denominators are 878,561
The GCF of 854,469 is 7 .
LCM of 878,561 is 492558.
The greatest common factor of 854/878,469/561 = [GCF of 854,469]/[LCM of 878,561]= 7/492558
Therefore, the GCF of 854/878,469/561 is 7/492558.
To find the highest common factor of 854,469, 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 469 are 1, 7, 67, 469
The HCF of 854,469 is 7.
Lets's calculate GCF of 854,469
7 | 854, 469 |
122, 67 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 854
:1,2,7,14,61,122,427,854
Now, list down the factors of 469
:1,7,67,469
Greatest Common Factor
We found the factors 854,469 . The biggest common factor number is the GCF number.
So the greatest common factor 854,469 is 7.
Lets's calculate LCM of 878,561
Given numbers has no common factors except 1. So, there LCM is their product i.e 492558
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/492558
Therefore, the GCF of Fractions 854/878,469/561 is 7/492558
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 878,561 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(878,561) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(878,561) x common factors =1 x 1 = 1
LCM(878,561) = ( 878 × 561 ) / 1
LCM(878,561) = 492558 / 1
LCM(878,561) = 492558
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 854,469?
The HCF of 854,469 is 7
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 854/878, 469/561?
Answer: GCF of Numerators as per given numbers 854/878, 469/561 is
GCF of Numerators i.e. for 854,469 is 7
LCM of denominators i.e. for 878,561 is 492558.
Thus, GCF of Fractions is 7/492558.Finally, GCF of Fractions for 854/878, 469/561 is 7/492558.