Use our free GCF of Fractions Calculator tool to compute the GCF of 872/409, 690/401 i.e 2/164009 easily. The following is the detailed procedure to determine the greatest common factor of fractions 872/409, 690/401.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 872/409,690/401
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 872/409,690/401, numerators are 872,690
Denominators are 409,401
The GCF of 872,690 is 2 .
LCM of 409,401 is 164009.
The greatest common factor of 872/409,690/401 = [GCF of 872,690]/[LCM of 409,401]= 2/164009
Therefore, the GCF of 872/409,690/401 is 2/164009.
To find the highest common factor of 872,690, we have to find the factors of both numbers and list the highest common factor.
The factors of 872 are 1, 2, 4, 8, 109, 218, 436, 872
The factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
The HCF of 872,690 is 2.
Lets's calculate GCF of 872,690
2 | 872, 690 |
436, 345 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 872
:1,2,4,8,109,218,436,872
Now, list down the factors of 690
:1,2,3,5,6,10,15,23,30,46,69,115,138,230,345,690
Greatest Common Factor
We found the factors 872,690 . The biggest common factor number is the GCF number.
So the greatest common factor 872,690 is 2.
Lets's calculate LCM of 409,401
Given numbers has no common factors except 1. So, there LCM is their product i.e 164009
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/164009
Therefore, the GCF of Fractions 872/409,690/401 is 2/164009
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 409,401 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,401) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,401) x common factors =1 x 1 = 1
LCM(409,401) = ( 409 × 401 ) / 1
LCM(409,401) = 164009 / 1
LCM(409,401) = 164009
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 872,690?
The HCF of 872,690 is 2
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 872/409, 690/401?
Answer: GCF of Numerators as per given numbers 872/409, 690/401 is
GCF of Numerators i.e. for 872,690 is 2
LCM of denominators i.e. for 409,401 is 164009.
Thus, GCF of Fractions is 2/164009.Finally, GCF of Fractions for 872/409, 690/401 is 2/164009.