What are the divisors of 5602?

1, 2, 2801, 5602

There is a total of 4 positive divisors.
The sum of these divisors is 8406.
The arithmetic mean is 2101.5.

2 even divisors

2, 5602

2 odd divisors

1, 2801

How to compute the divisors of 5602?

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 5602 by each of the numbers from 1 to 5602 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)

5602 / 1 = 5602 (the remainder is 0, so 1 is a divisor of 5602)
5602 / 2 = 2801 (the remainder is 0, so 2 is a divisor of 5602)
5602 / 3 = 1867.3333333333 (the remainder is 1, so 3 is not a divisor of 5602)
...
5602 / 5601 = 1.0001785395465 (the remainder is 1, so 5601 is not a divisor of 5602)
5602 / 5602 = 1 (the remainder is 0, so 5602 is a divisor of 5602)

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 5602 (i.e. 74.846509604657). 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 $\frac{N}{d} = D$ )

5602 / 1 = 5602 (the remainder is 0, so 1 and 5602 are divisors of 5602)
5602 / 2 = 2801 (the remainder is 0, so 2 and 2801 are divisors of 5602)
5602 / 3 = 1867.3333333333 (the remainder is 1, so 3 is not a divisor of 5602)
...
5602 / 73 = 76.739726027397 (the remainder is 54, so 73 is not a divisor of 5602)
5602 / 74 = 75.702702702703 (the remainder is 52, so 74 is not a divisor of 5602)