Use our free GCF of Fractions Calculator tool to compute the GCF of 36/84, 422/17, 231/309 i.e 1/147084 easily. The following is the detailed procedure to determine the greatest common factor of fractions 36/84, 422/17, 231/309.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 36/84,422/17,231/309
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 36/84,422/17,231/309, numerators are 36,422,231
Denominators are 84,17,309
The GCF of 36,422,231 is 1 .
LCM of 84,17,309 is 147084.
The greatest common factor of 36/84,422/17,231/309 = [GCF of 36,422,231]/[LCM of 84,17,309]= 1/147084
Therefore, the GCF of 36/84,422/17,231/309 is 1/147084.
To find the highest common factor of 36,422,231, we have to find the factors of both numbers and list the highest common factor.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 422 are 1, 2, 211, 422
The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231
The HCF of 36,422,231 is 1.
Lets's calculate GCF of 36,422,231
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 36
:1,2,3,4,6,9,12,18,36
Now, list down the factors of 422
:1,2,211,422
Now, list down the factors of 231
:1,3,7,11,21,33,77,231
Greatest Common Factor
We found the factors 36,422,231 . The biggest common factor number is the GCF number.
So the greatest common factor 36,422,231 is 1.
Lets's calculate LCM of 84,17,309
3 | 84, 17, 309 |
28, 17, 103 |
∴ So the LCM of the given numbers is 3 x 28 x 17 x 103 = 147084
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/147084
Therefore, the GCF of Fractions 36/84,422/17,231/309 is 1/147084
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 84,17,309 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,17,309) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(84,17,309) x common factors =1 x 3 = 3
LCM(84,17,309) = ( 84 × 17 × 309 ) / 3
LCM(84,17,309) = 441252 / 3
LCM(84,17,309) = 147084
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 36,422,231?
The HCF of 36,422,231 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 36/84, 422/17, 231/309?
Answer: GCF of Numerators as per given numbers 36/84, 422/17, 231/309 is
GCF of Numerators i.e. for 36,422,231 is 1
LCM of denominators i.e. for 84,17,309 is 147084.
Thus, GCF of Fractions is 1/147084.Finally, GCF of Fractions for 36/84, 422/17, 231/309 is 1/147084.