Use our free GCF of Fractions Calculator tool to compute the GCF of 21/399, 61/574, 309/189 i.e 1/294462 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/399, 61/574, 309/189.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 21/399,61/574,309/189
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 21/399,61/574,309/189, numerators are 21,61,309
Denominators are 399,574,189
The GCF of 21,61,309 is 1 .
LCM of 399,574,189 is 294462.
The greatest common factor of 21/399,61/574,309/189 = [GCF of 21,61,309]/[LCM of 399,574,189]= 1/294462
Therefore, the GCF of 21/399,61/574,309/189 is 1/294462.
To find the highest common factor of 21,61,309, 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 61 are 1, 61
The factors of 309 are 1, 3, 103, 309
The HCF of 21,61,309 is 1.
Lets's calculate GCF of 21,61,309
∴ 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 61
:1,61
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 21,61,309 . The biggest common factor number is the GCF number.
So the greatest common factor 21,61,309 is 1.
Lets's calculate LCM of 399,574,189
3 | 399, 574, 189 |
7 | 133, 574, 63 |
19, 82, 9 |
∴ So the LCM of the given numbers is 3 x 7 x 19 x 82 x 9 = 294462
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/294462
Therefore, the GCF of Fractions 21/399,61/574,309/189 is 1/294462
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 399,574,189 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(399,574,189) = 7
common factors(in case of two or more numbers have common factors) = 21
GCF(399,574,189) x common factors =7 x 21 = 147
LCM(399,574,189) = ( 399 × 574 × 189 ) / 147
LCM(399,574,189) = 43285914 / 147
LCM(399,574,189) = 294462
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 21,61,309?
The HCF of 21,61,309 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 21/399, 61/574, 309/189?
Answer: GCF of Numerators as per given numbers 21/399, 61/574, 309/189 is
GCF of Numerators i.e. for 21,61,309 is 1
LCM of denominators i.e. for 399,574,189 is 294462.
Thus, GCF of Fractions is 1/294462.Finally, GCF of Fractions for 21/399, 61/574, 309/189 is 1/294462.