What are the divisors of 552?

1, 2, 3, 4, 6, 8, 12, 23, 24, 46, 69, 92, 138, 184, 276, 552

There is a total of 16 positive divisors.
The sum of these divisors is 1440.
The arithmetic mean is 90.

12 even divisors

2, 4, 6, 8, 12, 24, 46, 92, 138, 184, 276, 552

4 odd divisors

1, 3, 23, 69

How to compute the divisors of 552?

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 552 by each of the numbers from 1 to 552 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)

552 / 1 = 552 (the remainder is 0, so 1 is a divisor of 552)
552 / 2 = 276 (the remainder is 0, so 2 is a divisor of 552)
552 / 3 = 184 (the remainder is 0, so 3 is a divisor of 552)
...
552 / 551 = 1.0018148820327 (the remainder is 1, so 551 is not a divisor of 552)
552 / 552 = 1 (the remainder is 0, so 552 is a divisor of 552)

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 552 (i.e. 23.494680248941). 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 $\frac{N}{d} = D$ )

552 / 1 = 552 (the remainder is 0, so 1 and 552 are divisors of 552)
552 / 2 = 276 (the remainder is 0, so 2 and 276 are divisors of 552)
552 / 3 = 184 (the remainder is 0, so 3 and 184 are divisors of 552)
...
552 / 22 = 25.090909090909 (the remainder is 2, so 22 is not a divisor of 552)
552 / 23 = 24 (the remainder is 0, so 23 and 24 are divisors of 552)