What are the divisors of 3016?

1, 2, 4, 8, 13, 26, 29, 52, 58, 104, 116, 232, 377, 754, 1508, 3016

There is a total of 16 positive divisors.
The sum of these divisors is 6300.
The arithmetic mean is 393.75.

12 even divisors

2, 4, 8, 26, 52, 58, 104, 116, 232, 754, 1508, 3016

4 odd divisors

1, 13, 29, 377

How to compute the divisors of 3016?

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 3016 by each of the numbers from 1 to 3016 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)

3016 / 1 = 3016 (the remainder is 0, so 1 is a divisor of 3016)
3016 / 2 = 1508 (the remainder is 0, so 2 is a divisor of 3016)
3016 / 3 = 1005.3333333333 (the remainder is 1, so 3 is not a divisor of 3016)
...
3016 / 3015 = 1.0003316749585 (the remainder is 1, so 3015 is not a divisor of 3016)
3016 / 3016 = 1 (the remainder is 0, so 3016 is a divisor of 3016)

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 3016 (i.e. 54.918120870984). 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 $\frac{N}{d} = D$ )

3016 / 1 = 3016 (the remainder is 0, so 1 and 3016 are divisors of 3016)
3016 / 2 = 1508 (the remainder is 0, so 2 and 1508 are divisors of 3016)
3016 / 3 = 1005.3333333333 (the remainder is 1, so 3 is not a divisor of 3016)
...
3016 / 53 = 56.905660377358 (the remainder is 48, so 53 is not a divisor of 3016)
3016 / 54 = 55.851851851852 (the remainder is 46, so 54 is not a divisor of 3016)