What are the divisors of 2943?
1, 3, 9, 27, 109, 327, 981, 2943
- There is a total of 8 positive divisors.
- The sum of these divisors is 4400.
- The arithmetic mean is 550.
8 odd divisors
1, 3, 9, 27, 109, 327, 981, 2943
How to compute the divisors of 2943?
A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.
Brute force algorithm
We could start by using a brute-force method which would involve dividing 2943 by each of the numbers from 1 to 2943 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 2943 / 1 = 2943 (the remainder is 0, so 1 is a divisor of 2943)
- 2943 / 2 = 1471.5 (the remainder is 1, so 2 is not a divisor of 2943)
- 2943 / 3 = 981 (the remainder is 0, so 3 is a divisor of 2943)
- ...
- 2943 / 2942 = 1.0003399048266 (the remainder is 1, so 2942 is not a divisor of 2943)
- 2943 / 2943 = 1 (the remainder is 0, so 2943 is a divisor of 2943)
Improved algorithm using square-root
However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 2943 (i.e. 54.249423960075). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:
(thus, if , then )
- 2943 / 1 = 2943 (the remainder is 0, so 1 and 2943 are divisors of 2943)
- 2943 / 2 = 1471.5 (the remainder is 1, so 2 is not a divisor of 2943)
- 2943 / 3 = 981 (the remainder is 0, so 3 and 981 are divisors of 2943)
- ...
- 2943 / 53 = 55.528301886792 (the remainder is 28, so 53 is not a divisor of 2943)
- 2943 / 54 = 54.5 (the remainder is 27, so 54 is not a divisor of 2943)