Use our free GCF of Fractions Calculator tool to compute the GCF of 185/126, 470/195 i.e 5/8190 easily. The following is the detailed procedure to determine the greatest common factor of fractions 185/126, 470/195.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 185/126,470/195
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 185/126,470/195, numerators are 185,470
Denominators are 126,195
The GCF of 185,470 is 5 .
LCM of 126,195 is 8190.
The greatest common factor of 185/126,470/195 = [GCF of 185,470]/[LCM of 126,195]= 5/8190
Therefore, the GCF of 185/126,470/195 is 5/8190.
To find the highest common factor of 185,470, we have to find the factors of both numbers and list the highest common factor.
The factors of 185 are 1, 5, 37, 185
The factors of 470 are 1, 2, 5, 10, 47, 94, 235, 470
The HCF of 185,470 is 5.
Lets's calculate GCF of 185,470
5 | 185, 470 |
37, 94 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 185
:1,5,37,185
Now, list down the factors of 470
:1,2,5,10,47,94,235,470
Greatest Common Factor
We found the factors 185,470 . The biggest common factor number is the GCF number.
So the greatest common factor 185,470 is 5.
Lets's calculate LCM of 126,195
3 | 126, 195 |
42, 65 |
∴ So the LCM of the given numbers is 3 x 42 x 65 = 8190
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/8190
Therefore, the GCF of Fractions 185/126,470/195 is 5/8190
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 126,195 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(126,195) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(126,195) x common factors =3 x 1 = 3
LCM(126,195) = ( 126 × 195 ) / 3
LCM(126,195) = 24570 / 3
LCM(126,195) = 8190
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 185,470?
The HCF of 185,470 is 5
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 185/126, 470/195?
Answer: GCF of Numerators as per given numbers 185/126, 470/195 is
GCF of Numerators i.e. for 185,470 is 5
LCM of denominators i.e. for 126,195 is 8190.
Thus, GCF of Fractions is 5/8190.Finally, GCF of Fractions for 185/126, 470/195 is 5/8190.