Use our free GCF of Fractions Calculator tool to compute the GCF of 43/351, 51/756, 210/606 i.e 1/992628 easily. The following is the detailed procedure to determine the greatest common factor of fractions 43/351, 51/756, 210/606.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 43/351,51/756,210/606
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 43/351,51/756,210/606, numerators are 43,51,210
Denominators are 351,756,606
The GCF of 43,51,210 is 1 .
LCM of 351,756,606 is 992628.
The greatest common factor of 43/351,51/756,210/606 = [GCF of 43,51,210]/[LCM of 351,756,606]= 1/992628
Therefore, the GCF of 43/351,51/756,210/606 is 1/992628.
To find the highest common factor of 43,51,210, we have to find the factors of both numbers and list the highest common factor.
The factors of 43 are 1, 43
The factors of 51 are 1, 3, 17, 51
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The HCF of 43,51,210 is 1.
Lets's calculate GCF of 43,51,210
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 43
:1,43
Now, list down the factors of 51
:1,3,17,51
Now, list down the factors of 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Greatest Common Factor
We found the factors 43,51,210 . The biggest common factor number is the GCF number.
So the greatest common factor 43,51,210 is 1.
Lets's calculate LCM of 351,756,606
2 | 351, 756, 606 |
3 | 351, 378, 303 |
3 | 117, 126, 101 |
3 | 39, 42, 101 |
13, 14, 101 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 13 x 14 x 101 = 992628
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/992628
Therefore, the GCF of Fractions 43/351,51/756,210/606 is 1/992628
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 351,756,606 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(351,756,606) = 3
common factors(in case of two or more numbers have common factors) = 54
GCF(351,756,606) x common factors =3 x 54 = 162
LCM(351,756,606) = ( 351 × 756 × 606 ) / 162
LCM(351,756,606) = 160805736 / 162
LCM(351,756,606) = 992628
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 43,51,210?
The HCF of 43,51,210 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 43/351, 51/756, 210/606?
Answer: GCF of Numerators as per given numbers 43/351, 51/756, 210/606 is
GCF of Numerators i.e. for 43,51,210 is 1
LCM of denominators i.e. for 351,756,606 is 992628.
Thus, GCF of Fractions is 1/992628.Finally, GCF of Fractions for 43/351, 51/756, 210/606 is 1/992628.