What are the divisors of 3032?

1, 2, 4, 8, 379, 758, 1516, 3032

There is a total of 8 positive divisors.
The sum of these divisors is 5700.
The arithmetic mean is 712.5.

6 even divisors

2, 4, 8, 758, 1516, 3032

2 odd divisors

1, 379

How to compute the divisors of 3032?

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 3032 by each of the numbers from 1 to 3032 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)

3032 / 1 = 3032 (the remainder is 0, so 1 is a divisor of 3032)
3032 / 2 = 1516 (the remainder is 0, so 2 is a divisor of 3032)
3032 / 3 = 1010.6666666667 (the remainder is 2, so 3 is not a divisor of 3032)
...
3032 / 3031 = 1.0003299241175 (the remainder is 1, so 3031 is not a divisor of 3032)
3032 / 3032 = 1 (the remainder is 0, so 3032 is a divisor of 3032)

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 3032 (i.e. 55.063599591745). 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 $\frac{N}{d} = D$ )

3032 / 1 = 3032 (the remainder is 0, so 1 and 3032 are divisors of 3032)
3032 / 2 = 1516 (the remainder is 0, so 2 and 1516 are divisors of 3032)
3032 / 3 = 1010.6666666667 (the remainder is 2, so 3 is not a divisor of 3032)
...
3032 / 54 = 56.148148148148 (the remainder is 8, so 54 is not a divisor of 3032)
3032 / 55 = 55.127272727273 (the remainder is 7, so 55 is not a divisor of 3032)