What are the divisors of 5552?

1, 2, 4, 8, 16, 347, 694, 1388, 2776, 5552

There is a total of 10 positive divisors.
The sum of these divisors is 10788.
The arithmetic mean is 1078.8.

8 even divisors

2, 4, 8, 16, 694, 1388, 2776, 5552

2 odd divisors

1, 347

How to compute the divisors of 5552?

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 5552 by each of the numbers from 1 to 5552 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)

5552 / 1 = 5552 (the remainder is 0, so 1 is a divisor of 5552)
5552 / 2 = 2776 (the remainder is 0, so 2 is a divisor of 5552)
5552 / 3 = 1850.6666666667 (the remainder is 2, so 3 is not a divisor of 5552)
...
5552 / 5551 = 1.0001801477211 (the remainder is 1, so 5551 is not a divisor of 5552)
5552 / 5552 = 1 (the remainder is 0, so 5552 is a divisor of 5552)

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 5552 (i.e. 74.511744040789). 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 $\frac{N}{d} = D$ )

5552 / 1 = 5552 (the remainder is 0, so 1 and 5552 are divisors of 5552)
5552 / 2 = 2776 (the remainder is 0, so 2 and 2776 are divisors of 5552)
5552 / 3 = 1850.6666666667 (the remainder is 2, so 3 is not a divisor of 5552)
...
5552 / 73 = 76.054794520548 (the remainder is 4, so 73 is not a divisor of 5552)
5552 / 74 = 75.027027027027 (the remainder is 2, so 74 is not a divisor of 5552)