Use our free GCF of Fractions Calculator tool to compute the GCF of 20/320, 86/446, 231/212 i.e 1/3782080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 20/320, 86/446, 231/212.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 20/320,86/446,231/212
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 20/320,86/446,231/212, numerators are 20,86,231
Denominators are 320,446,212
The GCF of 20,86,231 is 1 .
LCM of 320,446,212 is 3782080.
The greatest common factor of 20/320,86/446,231/212 = [GCF of 20,86,231]/[LCM of 320,446,212]= 1/3782080
Therefore, the GCF of 20/320,86/446,231/212 is 1/3782080.
To find the highest common factor of 20,86,231, we have to find the factors of both numbers and list the highest common factor.
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 86 are 1, 2, 43, 86
The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231
The HCF of 20,86,231 is 1.
Lets's calculate GCF of 20,86,231
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 20
:1,2,4,5,10,20
Now, list down the factors of 86
:1,2,43,86
Now, list down the factors of 231
:1,3,7,11,21,33,77,231
Greatest Common Factor
We found the factors 20,86,231 . The biggest common factor number is the GCF number.
So the greatest common factor 20,86,231 is 1.
Lets's calculate LCM of 320,446,212
2 | 320, 446, 212 |
2 | 160, 223, 106 |
80, 223, 53 |
∴ So the LCM of the given numbers is 2 x 2 x 80 x 223 x 53 = 3782080
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3782080
Therefore, the GCF of Fractions 20/320,86/446,231/212 is 1/3782080
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 320,446,212 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(320,446,212) = 2
common factors(in case of two or more numbers have common factors) = 4
GCF(320,446,212) x common factors =2 x 4 = 8
LCM(320,446,212) = ( 320 × 446 × 212 ) / 8
LCM(320,446,212) = 30256640 / 8
LCM(320,446,212) = 3782080
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 20,86,231?
The HCF of 20,86,231 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 20/320, 86/446, 231/212?
Answer: GCF of Numerators as per given numbers 20/320, 86/446, 231/212 is
GCF of Numerators i.e. for 20,86,231 is 1
LCM of denominators i.e. for 320,446,212 is 3782080.
Thus, GCF of Fractions is 1/3782080.Finally, GCF of Fractions for 20/320, 86/446, 231/212 is 1/3782080.