What are the divisors of 533?

1, 13, 41, 533

There is a total of 4 positive divisors.
The sum of these divisors is 588.
The arithmetic mean is 147.

4 odd divisors

1, 13, 41, 533

How to compute the divisors of 533?

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 533 by each of the numbers from 1 to 533 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)

533 / 1 = 533 (the remainder is 0, so 1 is a divisor of 533)
533 / 2 = 266.5 (the remainder is 1, so 2 is not a divisor of 533)
533 / 3 = 177.66666666667 (the remainder is 2, so 3 is not a divisor of 533)
...
533 / 532 = 1.0018796992481 (the remainder is 1, so 532 is not a divisor of 533)
533 / 533 = 1 (the remainder is 0, so 533 is a divisor of 533)

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 533 (i.e. 23.08679276123). 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 $\frac{N}{d} = D$ )

533 / 1 = 533 (the remainder is 0, so 1 and 533 are divisors of 533)
533 / 2 = 266.5 (the remainder is 1, so 2 is not a divisor of 533)
533 / 3 = 177.66666666667 (the remainder is 2, so 3 is not a divisor of 533)
...
533 / 22 = 24.227272727273 (the remainder is 5, so 22 is not a divisor of 533)
533 / 23 = 23.173913043478 (the remainder is 4, so 23 is not a divisor of 533)