Use our free GCF of Fractions Calculator tool to compute the GCF of 17/432, 419/100, 211/978 i.e 1/1760400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/432, 419/100, 211/978.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 17/432,419/100,211/978
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 17/432,419/100,211/978, numerators are 17,419,211
Denominators are 432,100,978
The GCF of 17,419,211 is 1 .
LCM of 432,100,978 is 1760400.
The greatest common factor of 17/432,419/100,211/978 = [GCF of 17,419,211]/[LCM of 432,100,978]= 1/1760400
Therefore, the GCF of 17/432,419/100,211/978 is 1/1760400.
To find the highest common factor of 17,419,211, we have to find the factors of both numbers and list the highest common factor.
The factors of 17 are 1, 17
The factors of 419 are 1, 419
The factors of 211 are 1, 211
The HCF of 17,419,211 is 1.
Lets's calculate GCF of 17,419,211
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 17
:1,17
Now, list down the factors of 419
:1,419
Now, list down the factors of 211
:1,211
Greatest Common Factor
We found the factors 17,419,211 . The biggest common factor number is the GCF number.
So the greatest common factor 17,419,211 is 1.
Lets's calculate LCM of 432,100,978
2 | 432, 100, 978 |
2 | 216, 50, 489 |
3 | 108, 25, 489 |
36, 25, 163 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 36 x 25 x 163 = 1760400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1760400
Therefore, the GCF of Fractions 17/432,419/100,211/978 is 1/1760400
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 432,100,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(432,100,978) = 2
common factors(in case of two or more numbers have common factors) = 12
GCF(432,100,978) x common factors =2 x 12 = 24
LCM(432,100,978) = ( 432 × 100 × 978 ) / 24
LCM(432,100,978) = 42249600 / 24
LCM(432,100,978) = 1760400
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 17,419,211?
The HCF of 17,419,211 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 17/432, 419/100, 211/978?
Answer: GCF of Numerators as per given numbers 17/432, 419/100, 211/978 is
GCF of Numerators i.e. for 17,419,211 is 1
LCM of denominators i.e. for 432,100,978 is 1760400.
Thus, GCF of Fractions is 1/1760400.Finally, GCF of Fractions for 17/432, 419/100, 211/978 is 1/1760400.