Use our free GCF of Fractions Calculator tool to compute the GCF of 34/459, 72/306, 405/627 i.e 1/191862 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/459, 72/306, 405/627.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 34/459,72/306,405/627
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 34/459,72/306,405/627, numerators are 34,72,405
Denominators are 459,306,627
The GCF of 34,72,405 is 1 .
LCM of 459,306,627 is 191862.
The greatest common factor of 34/459,72/306,405/627 = [GCF of 34,72,405]/[LCM of 459,306,627]= 1/191862
Therefore, the GCF of 34/459,72/306,405/627 is 1/191862.
To find the highest common factor of 34,72,405, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The HCF of 34,72,405 is 1.
Lets's calculate GCF of 34,72,405
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Greatest Common Factor
We found the factors 34,72,405 . The biggest common factor number is the GCF number.
So the greatest common factor 34,72,405 is 1.
Lets's calculate LCM of 459,306,627
3 | 459, 306, 627 |
3 | 153, 102, 209 |
17 | 51, 34, 209 |
3, 2, 209 |
∴ So the LCM of the given numbers is 3 x 3 x 17 x 3 x 2 x 209 = 191862
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/191862
Therefore, the GCF of Fractions 34/459,72/306,405/627 is 1/191862
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 459,306,627 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(459,306,627) = 3
common factors(in case of two or more numbers have common factors) = 153
GCF(459,306,627) x common factors =3 x 153 = 459
LCM(459,306,627) = ( 459 × 306 × 627 ) / 459
LCM(459,306,627) = 88064658 / 459
LCM(459,306,627) = 191862
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 34,72,405?
The HCF of 34,72,405 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 34/459, 72/306, 405/627?
Answer: GCF of Numerators as per given numbers 34/459, 72/306, 405/627 is
GCF of Numerators i.e. for 34,72,405 is 1
LCM of denominators i.e. for 459,306,627 is 191862.
Thus, GCF of Fractions is 1/191862.Finally, GCF of Fractions for 34/459, 72/306, 405/627 is 1/191862.