What are the divisors of 3029?

1, 13, 233, 3029

There is a total of 4 positive divisors.
The sum of these divisors is 3276.
The arithmetic mean is 819.

4 odd divisors

1, 13, 233, 3029

How to compute the divisors of 3029?

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.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 3029 by each of the numbers from 1 to 3029 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

3029 / 1 = 3029 (the remainder is 0, so 1 is a divisor of 3029)
3029 / 2 = 1514.5 (the remainder is 1, so 2 is not a divisor of 3029)
3029 / 3 = 1009.6666666667 (the remainder is 2, so 3 is not a divisor of 3029)
...
3029 / 3028 = 1.0003302509908 (the remainder is 1, so 3028 is not a divisor of 3029)
3029 / 3029 = 1 (the remainder is 0, so 3029 is a divisor of 3029)

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 3029 (i.e. 55.036351623268). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

3029 / 1 = 3029 (the remainder is 0, so 1 and 3029 are divisors of 3029)
3029 / 2 = 1514.5 (the remainder is 1, so 2 is not a divisor of 3029)
3029 / 3 = 1009.6666666667 (the remainder is 2, so 3 is not a divisor of 3029)
...
3029 / 54 = 56.092592592593 (the remainder is 5, so 54 is not a divisor of 3029)
3029 / 55 = 55.072727272727 (the remainder is 4, so 55 is not a divisor of 3029)