Use our free GCF of Fractions Calculator tool to compute the GCF of 765/38, 729/350 i.e 9/6650 easily. The following is the detailed procedure to determine the greatest common factor of fractions 765/38, 729/350.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 765/38,729/350
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 765/38,729/350, numerators are 765,729
Denominators are 38,350
The GCF of 765,729 is 9 .
LCM of 38,350 is 6650.
The greatest common factor of 765/38,729/350 = [GCF of 765,729]/[LCM of 38,350]= 9/6650
Therefore, the GCF of 765/38,729/350 is 9/6650.
To find the highest common factor of 765,729, we have to find the factors of both numbers and list the highest common factor.
The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
The factors of 729 are 1, 3, 9, 27, 81, 243, 729
The HCF of 765,729 is 9.
Lets's calculate GCF of 765,729
3 | 765, 729 |
3 | 255, 243 |
85, 81 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Now, list down the factors of 765
:1,3,5,9,15,17,45,51,85,153,255,765
Now, list down the factors of 729
:1,3,9,27,81,243,729
Greatest Common Factor
We found the factors 765,729 . The biggest common factor number is the GCF number.
So the greatest common factor 765,729 is 9.
Lets's calculate LCM of 38,350
2 | 38, 350 |
19, 175 |
∴ So the LCM of the given numbers is 2 x 19 x 175 = 6650
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/6650
Therefore, the GCF of Fractions 765/38,729/350 is 9/6650
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 38,350 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(38,350) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(38,350) x common factors =2 x 1 = 2
LCM(38,350) = ( 38 × 350 ) / 2
LCM(38,350) = 13300 / 2
LCM(38,350) = 6650
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 765,729?
The HCF of 765,729 is 9
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 765/38, 729/350?
Answer: GCF of Numerators as per given numbers 765/38, 729/350 is
GCF of Numerators i.e. for 765,729 is 9
LCM of denominators i.e. for 38,350 is 6650.
Thus, GCF of Fractions is 9/6650.Finally, GCF of Fractions for 765/38, 729/350 is 9/6650.