Use our free GCF of Fractions Calculator tool to compute the GCF of 698/409, 175/413 i.e 1/168917 easily. The following is the detailed procedure to determine the greatest common factor of fractions 698/409, 175/413.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 698/409,175/413
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 698/409,175/413, numerators are 698,175
Denominators are 409,413
The GCF of 698,175 is 1 .
LCM of 409,413 is 168917.
The greatest common factor of 698/409,175/413 = [GCF of 698,175]/[LCM of 409,413]= 1/168917
Therefore, the GCF of 698/409,175/413 is 1/168917.
To find the highest common factor of 698,175, we have to find the factors of both numbers and list the highest common factor.
The factors of 698 are 1, 2, 349, 698
The factors of 175 are 1, 5, 7, 25, 35, 175
The HCF of 698,175 is 1.
Lets's calculate GCF of 698,175
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 698
:1,2,349,698
Now, list down the factors of 175
:1,5,7,25,35,175
Greatest Common Factor
We found the factors 698,175 . The biggest common factor number is the GCF number.
So the greatest common factor 698,175 is 1.
Lets's calculate LCM of 409,413
Given numbers has no common factors except 1. So, there LCM is their product i.e 168917
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/168917
Therefore, the GCF of Fractions 698/409,175/413 is 1/168917
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 409,413 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,413) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,413) x common factors =1 x 1 = 1
LCM(409,413) = ( 409 × 413 ) / 1
LCM(409,413) = 168917 / 1
LCM(409,413) = 168917
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 698,175?
The HCF of 698,175 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 698/409, 175/413?
Answer: GCF of Numerators as per given numbers 698/409, 175/413 is
GCF of Numerators i.e. for 698,175 is 1
LCM of denominators i.e. for 409,413 is 168917.
Thus, GCF of Fractions is 1/168917.Finally, GCF of Fractions for 698/409, 175/413 is 1/168917.