What are the divisors of 3537?

1, 3, 9, 27, 131, 393, 1179, 3537

There is a total of 8 positive divisors.
The sum of these divisors is 5280.
The arithmetic mean is 660.

8 odd divisors

1, 3, 9, 27, 131, 393, 1179, 3537

How to compute the divisors of 3537?

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 3537 by each of the numbers from 1 to 3537 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)

3537 / 1 = 3537 (the remainder is 0, so 1 is a divisor of 3537)
3537 / 2 = 1768.5 (the remainder is 1, so 2 is not a divisor of 3537)
3537 / 3 = 1179 (the remainder is 0, so 3 is a divisor of 3537)
...
3537 / 3536 = 1.0002828054299 (the remainder is 1, so 3536 is not a divisor of 3537)
3537 / 3537 = 1 (the remainder is 0, so 3537 is a divisor of 3537)

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 3537 (i.e. 59.472682804797). 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 $\frac{N}{d} = D$ )

3537 / 1 = 3537 (the remainder is 0, so 1 and 3537 are divisors of 3537)
3537 / 2 = 1768.5 (the remainder is 1, so 2 is not a divisor of 3537)
3537 / 3 = 1179 (the remainder is 0, so 3 and 1179 are divisors of 3537)
...
3537 / 58 = 60.98275862069 (the remainder is 57, so 58 is not a divisor of 3537)
3537 / 59 = 59.949152542373 (the remainder is 56, so 59 is not a divisor of 3537)