GCF of 819/16, 105/706
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 819/16, 105/706 i.e 21/5648 easily. The following is the detailed procedure to determine the greatest common factor of fractions 819/16, 105/706.
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 819/16,105/706?
Given fractions are 819/16,105/706
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 819/16,105/706, numerators are 819,105
Denominators are 16,706
The GCF of 819,105 is 21 .
LCM of 16,706 is 5648.
The greatest common factor of 819/16,105/706 = [GCF of 819,105]/[LCM of 16,706]= 21/5648
Therefore, the GCF of 819/16,105/706 is 21/5648.
To find the highest common factor of 819,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 819,105 is 21.
Lets's calculate GCF of 819,105
| 3 | 819, 105 |
| 7 | 273, 35 |
| 39, 5 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 819,105 By Matching Biggest Common Factor Method
Now, list down the factors of 819
:1,3,7,9,13,21,39,63,91,117,273,819
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 819,105 . The biggest common factor number is the GCF number.
So the greatest common factor 819,105 is 21.
Lets's calculate LCM of 16,706
| 2 | 16, 706 |
| 8, 353 |
∴ So the LCM of the given numbers is 2 x 8 x 353 = 5648
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/5648
Therefore, the GCF of Fractions 819/16,105/706 is 21/5648
Least Common Multiple of 16,706 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 16,706 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,706) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(16,706) x common factors =2 x 1 = 2
LCM(16,706) = ( 16 × 706 ) / 2
LCM(16,706) = 11296 / 2
LCM(16,706) = 5648
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FAQs on GCF of Fractions of 819/16, 105/706
1. What is the HCF of 819,105?
The HCF of 819,105 is 21
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 819/16, 105/706?
Answer: GCF of Numerators as per given numbers 819/16, 105/706 is
GCF of Numerators i.e. for 819,105 is 21
LCM of denominators i.e. for 16,706 is 5648.
Thus, GCF of Fractions is 21/5648.Finally, GCF of Fractions for 819/16, 105/706 is 21/5648.