What are the divisors of 3277?

1, 29, 113, 3277

There is a total of 4 positive divisors.
The sum of these divisors is 3420.
The arithmetic mean is 855.

4 odd divisors

1, 29, 113, 3277

How to compute the divisors of 3277?

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 3277 by each of the numbers from 1 to 3277 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)

3277 / 1 = 3277 (the remainder is 0, so 1 is a divisor of 3277)
3277 / 2 = 1638.5 (the remainder is 1, so 2 is not a divisor of 3277)
3277 / 3 = 1092.3333333333 (the remainder is 1, so 3 is not a divisor of 3277)
...
3277 / 3276 = 1.0003052503053 (the remainder is 1, so 3276 is not a divisor of 3277)
3277 / 3277 = 1 (the remainder is 0, so 3277 is a divisor of 3277)

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 3277 (i.e. 57.245087125447). 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 $\frac{N}{d} = D$ )

3277 / 1 = 3277 (the remainder is 0, so 1 and 3277 are divisors of 3277)
3277 / 2 = 1638.5 (the remainder is 1, so 2 is not a divisor of 3277)
3277 / 3 = 1092.3333333333 (the remainder is 1, so 3 is not a divisor of 3277)
...
3277 / 56 = 58.517857142857 (the remainder is 29, so 56 is not a divisor of 3277)
3277 / 57 = 57.491228070175 (the remainder is 28, so 57 is not a divisor of 3277)