Use our free GCF of Fractions Calculator tool to compute the GCF of 432/219, 806/975 i.e 2/71175 easily. The following is the detailed procedure to determine the greatest common factor of fractions 432/219, 806/975.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 432/219,806/975
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 432/219,806/975, numerators are 432,806
Denominators are 219,975
The GCF of 432,806 is 2 .
LCM of 219,975 is 71175.
The greatest common factor of 432/219,806/975 = [GCF of 432,806]/[LCM of 219,975]= 2/71175
Therefore, the GCF of 432/219,806/975 is 2/71175.
To find the highest common factor of 432,806, we have to find the factors of both numbers and list the highest common factor.
The factors of 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
The factors of 806 are 1, 2, 13, 26, 31, 62, 403, 806
The HCF of 432,806 is 2.
Lets's calculate GCF of 432,806
2 | 432, 806 |
216, 403 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 432
:1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,108,144,216,432
Now, list down the factors of 806
:1,2,13,26,31,62,403,806
Greatest Common Factor
We found the factors 432,806 . The biggest common factor number is the GCF number.
So the greatest common factor 432,806 is 2.
Lets's calculate LCM of 219,975
3 | 219, 975 |
73, 325 |
∴ So the LCM of the given numbers is 3 x 73 x 325 = 71175
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/71175
Therefore, the GCF of Fractions 432/219,806/975 is 2/71175
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 219,975 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(219,975) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(219,975) x common factors =3 x 1 = 3
LCM(219,975) = ( 219 × 975 ) / 3
LCM(219,975) = 213525 / 3
LCM(219,975) = 71175
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 432,806?
The HCF of 432,806 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 432/219, 806/975?
Answer: GCF of Numerators as per given numbers 432/219, 806/975 is
GCF of Numerators i.e. for 432,806 is 2
LCM of denominators i.e. for 219,975 is 71175.
Thus, GCF of Fractions is 2/71175.Finally, GCF of Fractions for 432/219, 806/975 is 2/71175.