What are the divisors of 3263?

1, 13, 251, 3263

There is a total of 4 positive divisors.
The sum of these divisors is 3528.
The arithmetic mean is 882.

4 odd divisors

1, 13, 251, 3263

How to compute the divisors of 3263?

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 3263 by each of the numbers from 1 to 3263 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)

3263 / 1 = 3263 (the remainder is 0, so 1 is a divisor of 3263)
3263 / 2 = 1631.5 (the remainder is 1, so 2 is not a divisor of 3263)
3263 / 3 = 1087.6666666667 (the remainder is 2, so 3 is not a divisor of 3263)
...
3263 / 3262 = 1.0003065603924 (the remainder is 1, so 3262 is not a divisor of 3263)
3263 / 3263 = 1 (the remainder is 0, so 3263 is a divisor of 3263)

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 3263 (i.e. 57.122675007391). 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 $\frac{N}{d} = D$ )

3263 / 1 = 3263 (the remainder is 0, so 1 and 3263 are divisors of 3263)
3263 / 2 = 1631.5 (the remainder is 1, so 2 is not a divisor of 3263)
3263 / 3 = 1087.6666666667 (the remainder is 2, so 3 is not a divisor of 3263)
...
3263 / 56 = 58.267857142857 (the remainder is 15, so 56 is not a divisor of 3263)
3263 / 57 = 57.245614035088 (the remainder is 14, so 57 is not a divisor of 3263)