What are the divisors of 3247?

1, 17, 191, 3247

There is a total of 4 positive divisors.
The sum of these divisors is 3456.
The arithmetic mean is 864.

4 odd divisors

1, 17, 191, 3247

How to compute the divisors of 3247?

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 3247 by each of the numbers from 1 to 3247 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)

3247 / 1 = 3247 (the remainder is 0, so 1 is a divisor of 3247)
3247 / 2 = 1623.5 (the remainder is 1, so 2 is not a divisor of 3247)
3247 / 3 = 1082.3333333333 (the remainder is 1, so 3 is not a divisor of 3247)
...
3247 / 3246 = 1.0003080714726 (the remainder is 1, so 3246 is not a divisor of 3247)
3247 / 3247 = 1 (the remainder is 0, so 3247 is a divisor of 3247)

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 3247 (i.e. 56.982453439634). 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 $\frac{N}{d} = D$ )

3247 / 1 = 3247 (the remainder is 0, so 1 and 3247 are divisors of 3247)
3247 / 2 = 1623.5 (the remainder is 1, so 2 is not a divisor of 3247)
3247 / 3 = 1082.3333333333 (the remainder is 1, so 3 is not a divisor of 3247)
...
3247 / 55 = 59.036363636364 (the remainder is 2, so 55 is not a divisor of 3247)
3247 / 56 = 57.982142857143 (the remainder is 55, so 56 is not a divisor of 3247)