What are the divisors of 2072?

1, 2, 4, 7, 8, 14, 28, 37, 56, 74, 148, 259, 296, 518, 1036, 2072

There is a total of 16 positive divisors.
The sum of these divisors is 4560.
The arithmetic mean is 285.

12 even divisors

2, 4, 8, 14, 28, 56, 74, 148, 296, 518, 1036, 2072

4 odd divisors

1, 7, 37, 259

How to compute the divisors of 2072?

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 2072 by each of the numbers from 1 to 2072 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)

2072 / 1 = 2072 (the remainder is 0, so 1 is a divisor of 2072)
2072 / 2 = 1036 (the remainder is 0, so 2 is a divisor of 2072)
2072 / 3 = 690.66666666667 (the remainder is 2, so 3 is not a divisor of 2072)
...
2072 / 2071 = 1.0004828585225 (the remainder is 1, so 2071 is not a divisor of 2072)
2072 / 2072 = 1 (the remainder is 0, so 2072 is a divisor of 2072)

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 2072 (i.e. 45.519226706964). 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 $\frac{N}{d} = D$ )

2072 / 1 = 2072 (the remainder is 0, so 1 and 2072 are divisors of 2072)
2072 / 2 = 1036 (the remainder is 0, so 2 and 1036 are divisors of 2072)
2072 / 3 = 690.66666666667 (the remainder is 2, so 3 is not a divisor of 2072)
...
2072 / 44 = 47.090909090909 (the remainder is 4, so 44 is not a divisor of 2072)
2072 / 45 = 46.044444444444 (the remainder is 2, so 45 is not a divisor of 2072)