GCF of 786/442, 309/198
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 786/442, 309/198 i.e 3/43758 easily. The following is the detailed procedure to determine the greatest common factor of fractions 786/442, 309/198.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 786/442,309/198?
Given fractions are 786/442,309/198
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 786/442,309/198, numerators are 786,309
Denominators are 442,198
The GCF of 786,309 is 3 .
LCM of 442,198 is 43758.
The greatest common factor of 786/442,309/198 = [GCF of 786,309]/[LCM of 442,198]= 3/43758
Therefore, the GCF of 786/442,309/198 is 3/43758.
To find the highest common factor of 786,309, we have to find the factors of both numbers and list the highest common factor.
The factors of 786 are 1, 2, 3, 6, 131, 262, 393, 786
The factors of 309 are 1, 3, 103, 309
The HCF of 786,309 is 3.
Lets's calculate GCF of 786,309
| 3 | 786, 309 |
| 262, 103 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 786,309 By Matching Biggest Common Factor Method
Now, list down the factors of 786
:1,2,3,6,131,262,393,786
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 786,309 . The biggest common factor number is the GCF number.
So the greatest common factor 786,309 is 3.
Lets's calculate LCM of 442,198
| 2 | 442, 198 |
| 221, 99 |
∴ So the LCM of the given numbers is 2 x 221 x 99 = 43758
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/43758
Therefore, the GCF of Fractions 786/442,309/198 is 3/43758
Least Common Multiple of 442,198 with GCF Formula
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 442,198 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(442,198) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(442,198) x common factors =2 x 1 = 2
LCM(442,198) = ( 442 × 198 ) / 2
LCM(442,198) = 87516 / 2
LCM(442,198) = 43758
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 786/442, 309/198
1. What is the HCF of 786,309?
The HCF of 786,309 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 786/442, 309/198?
Answer: GCF of Numerators as per given numbers 786/442, 309/198 is
GCF of Numerators i.e. for 786,309 is 3
LCM of denominators i.e. for 442,198 is 43758.
Thus, GCF of Fractions is 3/43758.Finally, GCF of Fractions for 786/442, 309/198 is 3/43758.