Use our free GCF of Fractions Calculator tool to compute the GCF of 809/45, 839/85, 705/72 i.e 1/6120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 809/45, 839/85, 705/72.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 809/45,839/85,705/72
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 809/45,839/85,705/72, numerators are 809,839,705
Denominators are 45,85,72
The GCF of 809,839,705 is 1 .
LCM of 45,85,72 is 6120.
The greatest common factor of 809/45,839/85,705/72 = [GCF of 809,839,705]/[LCM of 45,85,72]= 1/6120
Therefore, the GCF of 809/45,839/85,705/72 is 1/6120.
To find the highest common factor of 809,839,705, we have to find the factors of both numbers and list the highest common factor.
The factors of 809 are 1, 809
The factors of 839 are 1, 839
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The HCF of 809,839,705 is 1.
Lets's calculate GCF of 809,839,705
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 809
:1,809
Now, list down the factors of 839
:1,839
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Greatest Common Factor
We found the factors 809,839,705 . The biggest common factor number is the GCF number.
So the greatest common factor 809,839,705 is 1.
Lets's calculate LCM of 45,85,72
3 | 45, 85, 72 |
3 | 15, 85, 24 |
5 | 5, 85, 8 |
1, 17, 8 |
∴ So the LCM of the given numbers is 3 x 3 x 5 x 1 x 17 x 8 = 6120
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6120
Therefore, the GCF of Fractions 809/45,839/85,705/72 is 1/6120
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 45,85,72 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(45,85,72) = 1
common factors(in case of two or more numbers have common factors) = 45
GCF(45,85,72) x common factors =1 x 45 = 45
LCM(45,85,72) = ( 45 × 85 × 72 ) / 45
LCM(45,85,72) = 275400 / 45
LCM(45,85,72) = 6120
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 809,839,705?
The HCF of 809,839,705 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 809/45, 839/85, 705/72?
Answer: GCF of Numerators as per given numbers 809/45, 839/85, 705/72 is
GCF of Numerators i.e. for 809,839,705 is 1
LCM of denominators i.e. for 45,85,72 is 6120.
Thus, GCF of Fractions is 1/6120.Finally, GCF of Fractions for 809/45, 839/85, 705/72 is 1/6120.