Use our free GCF of Fractions Calculator tool to compute the GCF of 873/422, 657/686 i.e 9/144746 easily. The following is the detailed procedure to determine the greatest common factor of fractions 873/422, 657/686.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 873/422,657/686
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 873/422,657/686, numerators are 873,657
Denominators are 422,686
The GCF of 873,657 is 9 .
LCM of 422,686 is 144746.
The greatest common factor of 873/422,657/686 = [GCF of 873,657]/[LCM of 422,686]= 9/144746
Therefore, the GCF of 873/422,657/686 is 9/144746.
To find the highest common factor of 873,657, we have to find the factors of both numbers and list the highest common factor.
The factors of 873 are 1, 3, 9, 97, 291, 873
The factors of 657 are 1, 3, 9, 73, 219, 657
The HCF of 873,657 is 9.
Lets's calculate GCF of 873,657
3 | 873, 657 |
3 | 291, 219 |
97, 73 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Now, list down the factors of 873
:1,3,9,97,291,873
Now, list down the factors of 657
:1,3,9,73,219,657
Greatest Common Factor
We found the factors 873,657 . The biggest common factor number is the GCF number.
So the greatest common factor 873,657 is 9.
Lets's calculate LCM of 422,686
2 | 422, 686 |
211, 343 |
∴ So the LCM of the given numbers is 2 x 211 x 343 = 144746
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/144746
Therefore, the GCF of Fractions 873/422,657/686 is 9/144746
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 422,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(422,686) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(422,686) x common factors =2 x 1 = 2
LCM(422,686) = ( 422 × 686 ) / 2
LCM(422,686) = 289492 / 2
LCM(422,686) = 144746
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 873,657?
The HCF of 873,657 is 9
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 873/422, 657/686?
Answer: GCF of Numerators as per given numbers 873/422, 657/686 is
GCF of Numerators i.e. for 873,657 is 9
LCM of denominators i.e. for 422,686 is 144746.
Thus, GCF of Fractions is 9/144746.Finally, GCF of Fractions for 873/422, 657/686 is 9/144746.