What are the divisors of 2832?

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 59, 118, 177, 236, 354, 472, 708, 944, 1416, 2832

There is a total of 20 positive divisors.
The sum of these divisors is 7440.
The arithmetic mean is 372.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 118, 236, 354, 472, 708, 944, 1416, 2832

4 odd divisors

1, 3, 59, 177

How to compute the divisors of 2832?

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 2832 by each of the numbers from 1 to 2832 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)

2832 / 1 = 2832 (the remainder is 0, so 1 is a divisor of 2832)
2832 / 2 = 1416 (the remainder is 0, so 2 is a divisor of 2832)
2832 / 3 = 944 (the remainder is 0, so 3 is a divisor of 2832)
...
2832 / 2831 = 1.0003532320735 (the remainder is 1, so 2831 is not a divisor of 2832)
2832 / 2832 = 1 (the remainder is 0, so 2832 is a divisor of 2832)

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 2832 (i.e. 53.2165387826). 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 $\frac{N}{d} = D$ )

2832 / 1 = 2832 (the remainder is 0, so 1 and 2832 are divisors of 2832)
2832 / 2 = 1416 (the remainder is 0, so 2 and 1416 are divisors of 2832)
2832 / 3 = 944 (the remainder is 0, so 3 and 944 are divisors of 2832)
...
2832 / 52 = 54.461538461538 (the remainder is 24, so 52 is not a divisor of 2832)
2832 / 53 = 53.433962264151 (the remainder is 23, so 53 is not a divisor of 2832)