What are the divisors of 541?

1, 541

There is a total of 2 positive divisors.
The sum of these divisors is 542.
The arithmetic mean is 271.

2 odd divisors

1, 541

How to compute the divisors of 541?

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 541 by each of the numbers from 1 to 541 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)

541 / 1 = 541 (the remainder is 0, so 1 is a divisor of 541)
541 / 2 = 270.5 (the remainder is 1, so 2 is not a divisor of 541)
541 / 3 = 180.33333333333 (the remainder is 1, so 3 is not a divisor of 541)
...
541 / 540 = 1.0018518518519 (the remainder is 1, so 540 is not a divisor of 541)
541 / 541 = 1 (the remainder is 0, so 541 is a divisor of 541)

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 541 (i.e. 23.259406699226). 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 $\frac{N}{d} = D$ )

541 / 1 = 541 (the remainder is 0, so 1 and 541 are divisors of 541)
541 / 2 = 270.5 (the remainder is 1, so 2 is not a divisor of 541)
541 / 3 = 180.33333333333 (the remainder is 1, so 3 is not a divisor of 541)
...
541 / 22 = 24.590909090909 (the remainder is 13, so 22 is not a divisor of 541)
541 / 23 = 23.521739130435 (the remainder is 12, so 23 is not a divisor of 541)