GCF of 286/409, 990/517
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 286/409, 990/517 i.e 22/211453 easily. The following is the detailed procedure to determine the greatest common factor of fractions 286/409, 990/517.
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 286/409,990/517?
Given fractions are 286/409,990/517
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 286/409,990/517, numerators are 286,990
Denominators are 409,517
The GCF of 286,990 is 22 .
LCM of 409,517 is 211453.
The greatest common factor of 286/409,990/517 = [GCF of 286,990]/[LCM of 409,517]= 22/211453
Therefore, the GCF of 286/409,990/517 is 22/211453.
To find the highest common factor of 286,990, we have to find the factors of both numbers and list the highest common factor.
The factors of 286 are 1, 2, 11, 13, 22, 26, 143, 286
The factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990
The HCF of 286,990 is 22.
Lets's calculate GCF of 286,990
| 2 | 286, 990 |
| 11 | 143, 495 |
| 13, 45 |
∴ So the GCF of the given numbers is 2 x 11 = 22
Greatest Common Factor of 286,990 By Matching Biggest Common Factor Method
Now, list down the factors of 286
:1,2,11,13,22,26,143,286
Now, list down the factors of 990
:1,2,3,5,6,9,10,11,15,18,22,30,33,45,55,66,90,99,110,165,198,330,495,990
Greatest Common Factor
We found the factors 286,990 . The biggest common factor number is the GCF number.
So the greatest common factor 286,990 is 22.
Lets's calculate LCM of 409,517
Given numbers has no common factors except 1. So, there LCM is their product i.e 211453
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/211453
Therefore, the GCF of Fractions 286/409,990/517 is 22/211453
Least Common Multiple of 409,517 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 409,517 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,517) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,517) x common factors =1 x 1 = 1
LCM(409,517) = ( 409 × 517 ) / 1
LCM(409,517) = 211453 / 1
LCM(409,517) = 211453
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FAQs on GCF of Fractions of 286/409, 990/517
1. What is the HCF of 286,990?
The HCF of 286,990 is 22
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 286/409, 990/517?
Answer: GCF of Numerators as per given numbers 286/409, 990/517 is
GCF of Numerators i.e. for 286,990 is 22
LCM of denominators i.e. for 409,517 is 211453.
Thus, GCF of Fractions is 22/211453.Finally, GCF of Fractions for 286/409, 990/517 is 22/211453.