Use our free GCF of Fractions Calculator tool to compute the GCF of 21/81, 421/42, 184/413 i.e 1/66906 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/81, 421/42, 184/413.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 21/81,421/42,184/413
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 21/81,421/42,184/413, numerators are 21,421,184
Denominators are 81,42,413
The GCF of 21,421,184 is 1 .
LCM of 81,42,413 is 66906.
The greatest common factor of 21/81,421/42,184/413 = [GCF of 21,421,184]/[LCM of 81,42,413]= 1/66906
Therefore, the GCF of 21/81,421/42,184/413 is 1/66906.
To find the highest common factor of 21,421,184, 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 421 are 1, 421
The factors of 184 are 1, 2, 4, 8, 23, 46, 92, 184
The HCF of 21,421,184 is 1.
Lets's calculate GCF of 21,421,184
∴ 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 421
:1,421
Now, list down the factors of 184
:1,2,4,8,23,46,92,184
Greatest Common Factor
We found the factors 21,421,184 . The biggest common factor number is the GCF number.
So the greatest common factor 21,421,184 is 1.
Lets's calculate LCM of 81,42,413
3 | 81, 42, 413 |
7 | 27, 14, 413 |
27, 2, 59 |
∴ So the LCM of the given numbers is 3 x 7 x 27 x 2 x 59 = 66906
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/66906
Therefore, the GCF of Fractions 21/81,421/42,184/413 is 1/66906
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 81,42,413 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(81,42,413) = 1
common factors(in case of two or more numbers have common factors) = 21
GCF(81,42,413) x common factors =1 x 21 = 21
LCM(81,42,413) = ( 81 × 42 × 413 ) / 21
LCM(81,42,413) = 1405026 / 21
LCM(81,42,413) = 66906
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 21,421,184?
The HCF of 21,421,184 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 21/81, 421/42, 184/413?
Answer: GCF of Numerators as per given numbers 21/81, 421/42, 184/413 is
GCF of Numerators i.e. for 21,421,184 is 1
LCM of denominators i.e. for 81,42,413 is 66906.
Thus, GCF of Fractions is 1/66906.Finally, GCF of Fractions for 21/81, 421/42, 184/413 is 1/66906.