Use our free GCF of Fractions Calculator tool to compute the GCF of 21/780, 351/440, 860/717 i.e 1/4101240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/780, 351/440, 860/717.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 21/780,351/440,860/717
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 21/780,351/440,860/717, numerators are 21,351,860
Denominators are 780,440,717
The GCF of 21,351,860 is 1 .
LCM of 780,440,717 is 4101240.
The greatest common factor of 21/780,351/440,860/717 = [GCF of 21,351,860]/[LCM of 780,440,717]= 1/4101240
Therefore, the GCF of 21/780,351/440,860/717 is 1/4101240.
To find the highest common factor of 21,351,860, we have to find the factors of both numbers and list the highest common factor.
The factors of 21 are 1, 3, 7, 21
The factors of 351 are 1, 3, 9, 13, 27, 39, 117, 351
The factors of 860 are 1, 2, 4, 5, 10, 20, 43, 86, 172, 215, 430, 860
The HCF of 21,351,860 is 1.
Lets's calculate GCF of 21,351,860
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 351
:1,3,9,13,27,39,117,351
Now, list down the factors of 860
:1,2,4,5,10,20,43,86,172,215,430,860
Greatest Common Factor
We found the factors 21,351,860 . The biggest common factor number is the GCF number.
So the greatest common factor 21,351,860 is 1.
Lets's calculate LCM of 780,440,717
2 | 780, 440, 717 |
2 | 390, 220, 717 |
3 | 195, 110, 717 |
5 | 65, 110, 239 |
13, 22, 239 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 13 x 22 x 239 = 4101240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4101240
Therefore, the GCF of Fractions 21/780,351/440,860/717 is 1/4101240
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 780,440,717 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(780,440,717) = 1
common factors(in case of two or more numbers have common factors) = 60
GCF(780,440,717) x common factors =1 x 60 = 60
LCM(780,440,717) = ( 780 × 440 × 717 ) / 60
LCM(780,440,717) = 246074400 / 60
LCM(780,440,717) = 4101240
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 21,351,860?
The HCF of 21,351,860 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 21/780, 351/440, 860/717?
Answer: GCF of Numerators as per given numbers 21/780, 351/440, 860/717 is
GCF of Numerators i.e. for 21,351,860 is 1
LCM of denominators i.e. for 780,440,717 is 4101240.
Thus, GCF of Fractions is 1/4101240.Finally, GCF of Fractions for 21/780, 351/440, 860/717 is 1/4101240.