Use our free GCF of Fractions Calculator tool to compute the GCF of 174/221, 463/861 i.e 1/190281 easily. The following is the detailed procedure to determine the greatest common factor of fractions 174/221, 463/861.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 174/221,463/861
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 174/221,463/861, numerators are 174,463
Denominators are 221,861
The GCF of 174,463 is 1 .
LCM of 221,861 is 190281.
The greatest common factor of 174/221,463/861 = [GCF of 174,463]/[LCM of 221,861]= 1/190281
Therefore, the GCF of 174/221,463/861 is 1/190281.
To find the highest common factor of 174,463, we have to find the factors of both numbers and list the highest common factor.
The factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174
The factors of 463 are 1, 463
The HCF of 174,463 is 1.
Lets's calculate GCF of 174,463
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 174
:1,2,3,6,29,58,87,174
Now, list down the factors of 463
:1,463
Greatest Common Factor
We found the factors 174,463 . The biggest common factor number is the GCF number.
So the greatest common factor 174,463 is 1.
Lets's calculate LCM of 221,861
Given numbers has no common factors except 1. So, there LCM is their product i.e 190281
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/190281
Therefore, the GCF of Fractions 174/221,463/861 is 1/190281
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 221,861 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(221,861) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(221,861) x common factors =1 x 1 = 1
LCM(221,861) = ( 221 × 861 ) / 1
LCM(221,861) = 190281 / 1
LCM(221,861) = 190281
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 174,463?
The HCF of 174,463 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 174/221, 463/861?
Answer: GCF of Numerators as per given numbers 174/221, 463/861 is
GCF of Numerators i.e. for 174,463 is 1
LCM of denominators i.e. for 221,861 is 190281.
Thus, GCF of Fractions is 1/190281.Finally, GCF of Fractions for 174/221, 463/861 is 1/190281.