What are the divisors of 3552?

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 37, 48, 74, 96, 111, 148, 222, 296, 444, 592, 888, 1184, 1776, 3552

There is a total of 24 positive divisors.
The sum of these divisors is 9576.
The arithmetic mean is 399.

20 even divisors

2, 4, 6, 8, 12, 16, 24, 32, 48, 74, 96, 148, 222, 296, 444, 592, 888, 1184, 1776, 3552

4 odd divisors

1, 3, 37, 111

How to compute the divisors of 3552?

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 3552 by each of the numbers from 1 to 3552 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)

3552 / 1 = 3552 (the remainder is 0, so 1 is a divisor of 3552)
3552 / 2 = 1776 (the remainder is 0, so 2 is a divisor of 3552)
3552 / 3 = 1184 (the remainder is 0, so 3 is a divisor of 3552)
...
3552 / 3551 = 1.0002816108139 (the remainder is 1, so 3551 is not a divisor of 3552)
3552 / 3552 = 1 (the remainder is 0, so 3552 is a divisor of 3552)

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 3552 (i.e. 59.598657703005). 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 $\frac{N}{d} = D$ )

3552 / 1 = 3552 (the remainder is 0, so 1 and 3552 are divisors of 3552)
3552 / 2 = 1776 (the remainder is 0, so 2 and 1776 are divisors of 3552)
3552 / 3 = 1184 (the remainder is 0, so 3 and 1184 are divisors of 3552)
...
3552 / 58 = 61.241379310345 (the remainder is 14, so 58 is not a divisor of 3552)
3552 / 59 = 60.203389830508 (the remainder is 12, so 59 is not a divisor of 3552)