What are the divisors of 3237?

1, 3, 13, 39, 83, 249, 1079, 3237

There is a total of 8 positive divisors.
The sum of these divisors is 4704.
The arithmetic mean is 588.

8 odd divisors

1, 3, 13, 39, 83, 249, 1079, 3237

How to compute the divisors of 3237?

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 3237 by each of the numbers from 1 to 3237 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)

3237 / 1 = 3237 (the remainder is 0, so 1 is a divisor of 3237)
3237 / 2 = 1618.5 (the remainder is 1, so 2 is not a divisor of 3237)
3237 / 3 = 1079 (the remainder is 0, so 3 is a divisor of 3237)
...
3237 / 3236 = 1.0003090234858 (the remainder is 1, so 3236 is not a divisor of 3237)
3237 / 3237 = 1 (the remainder is 0, so 3237 is a divisor of 3237)

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 3237 (i.e. 56.894639466298). 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 $\frac{N}{d} = D$ )

3237 / 1 = 3237 (the remainder is 0, so 1 and 3237 are divisors of 3237)
3237 / 2 = 1618.5 (the remainder is 1, so 2 is not a divisor of 3237)
3237 / 3 = 1079 (the remainder is 0, so 3 and 1079 are divisors of 3237)
...
3237 / 55 = 58.854545454545 (the remainder is 47, so 55 is not a divisor of 3237)
3237 / 56 = 57.803571428571 (the remainder is 45, so 56 is not a divisor of 3237)