What are the divisors of 545?

1, 5, 109, 545

There is a total of 4 positive divisors.
The sum of these divisors is 660.
The arithmetic mean is 165.

4 odd divisors

1, 5, 109, 545

How to compute the divisors of 545?

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 545 by each of the numbers from 1 to 545 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)

545 / 1 = 545 (the remainder is 0, so 1 is a divisor of 545)
545 / 2 = 272.5 (the remainder is 1, so 2 is not a divisor of 545)
545 / 3 = 181.66666666667 (the remainder is 2, so 3 is not a divisor of 545)
...
545 / 544 = 1.0018382352941 (the remainder is 1, so 544 is not a divisor of 545)
545 / 545 = 1 (the remainder is 0, so 545 is a divisor of 545)

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 545 (i.e. 23.345235059858). 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 $\frac{N}{d} = D$ )

545 / 1 = 545 (the remainder is 0, so 1 and 545 are divisors of 545)
545 / 2 = 272.5 (the remainder is 1, so 2 is not a divisor of 545)
545 / 3 = 181.66666666667 (the remainder is 2, so 3 is not a divisor of 545)
...
545 / 22 = 24.772727272727 (the remainder is 17, so 22 is not a divisor of 545)
545 / 23 = 23.695652173913 (the remainder is 16, so 23 is not a divisor of 545)