What are the divisors of 5573?

1, 5573

There is a total of 2 positive divisors.
The sum of these divisors is 5574.
The arithmetic mean is 2787.

2 odd divisors

1, 5573

How to compute the divisors of 5573?

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 5573 by each of the numbers from 1 to 5573 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)

5573 / 1 = 5573 (the remainder is 0, so 1 is a divisor of 5573)
5573 / 2 = 2786.5 (the remainder is 1, so 2 is not a divisor of 5573)
5573 / 3 = 1857.6666666667 (the remainder is 2, so 3 is not a divisor of 5573)
...
5573 / 5572 = 1.0001794687724 (the remainder is 1, so 5572 is not a divisor of 5573)
5573 / 5573 = 1 (the remainder is 0, so 5573 is a divisor of 5573)

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 5573 (i.e. 74.652528423356). 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 $\frac{N}{d} = D$ )

5573 / 1 = 5573 (the remainder is 0, so 1 and 5573 are divisors of 5573)
5573 / 2 = 2786.5 (the remainder is 1, so 2 is not a divisor of 5573)
5573 / 3 = 1857.6666666667 (the remainder is 2, so 3 is not a divisor of 5573)
...
5573 / 73 = 76.342465753425 (the remainder is 25, so 73 is not a divisor of 5573)
5573 / 74 = 75.310810810811 (the remainder is 23, so 74 is not a divisor of 5573)