Use our free GCF of Fractions Calculator tool to compute the GCF of 111/715, 309/765 i.e 3/109395 easily. The following is the detailed procedure to determine the greatest common factor of fractions 111/715, 309/765.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 111/715,309/765
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 111/715,309/765, numerators are 111,309
Denominators are 715,765
The GCF of 111,309 is 3 .
LCM of 715,765 is 109395.
The greatest common factor of 111/715,309/765 = [GCF of 111,309]/[LCM of 715,765]= 3/109395
Therefore, the GCF of 111/715,309/765 is 3/109395.
To find the highest common factor of 111,309, we have to find the factors of both numbers and list the highest common factor.
The factors of 111 are 1, 3, 37, 111
The factors of 309 are 1, 3, 103, 309
The HCF of 111,309 is 3.
Lets's calculate GCF of 111,309
3 | 111, 309 |
37, 103 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 111
:1,3,37,111
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 111,309 . The biggest common factor number is the GCF number.
So the greatest common factor 111,309 is 3.
Lets's calculate LCM of 715,765
5 | 715, 765 |
143, 153 |
∴ So the LCM of the given numbers is 5 x 143 x 153 = 109395
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/109395
Therefore, the GCF of Fractions 111/715,309/765 is 3/109395
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 715,765 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(715,765) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(715,765) x common factors =5 x 1 = 5
LCM(715,765) = ( 715 × 765 ) / 5
LCM(715,765) = 546975 / 5
LCM(715,765) = 109395
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 111,309?
The HCF of 111,309 is 3
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 111/715, 309/765?
Answer: GCF of Numerators as per given numbers 111/715, 309/765 is
GCF of Numerators i.e. for 111,309 is 3
LCM of denominators i.e. for 715,765 is 109395.
Thus, GCF of Fractions is 3/109395.Finally, GCF of Fractions for 111/715, 309/765 is 3/109395.