What are the divisors of 3439?
1, 19, 181, 3439
- There is a total of 4 positive divisors.
- The sum of these divisors is 3640.
- The arithmetic mean is 910.
4 odd divisors
1, 19, 181, 3439
How to compute the divisors of 3439?
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 3439 by each of the numbers from 1 to 3439 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 3439 / 1 = 3439 (the remainder is 0, so 1 is a divisor of 3439)
- 3439 / 2 = 1719.5 (the remainder is 1, so 2 is not a divisor of 3439)
- 3439 / 3 = 1146.3333333333 (the remainder is 1, so 3 is not a divisor of 3439)
- ...
- 3439 / 3438 = 1.000290866783 (the remainder is 1, so 3438 is not a divisor of 3439)
- 3439 / 3439 = 1 (the remainder is 0, so 3439 is a divisor of 3439)
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 3439 (i.e. 58.642987645583). 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 )
- 3439 / 1 = 3439 (the remainder is 0, so 1 and 3439 are divisors of 3439)
- 3439 / 2 = 1719.5 (the remainder is 1, so 2 is not a divisor of 3439)
- 3439 / 3 = 1146.3333333333 (the remainder is 1, so 3 is not a divisor of 3439)
- ...
- 3439 / 57 = 60.333333333333 (the remainder is 19, so 57 is not a divisor of 3439)
- 3439 / 58 = 59.293103448276 (the remainder is 17, so 58 is not a divisor of 3439)