What are the divisors of 3501?

1, 3, 9, 389, 1167, 3501

There is a total of 6 positive divisors.
The sum of these divisors is 5070.
The arithmetic mean is 845.

6 odd divisors

1, 3, 9, 389, 1167, 3501

How to compute the divisors of 3501?

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 3501 by each of the numbers from 1 to 3501 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)

3501 / 1 = 3501 (the remainder is 0, so 1 is a divisor of 3501)
3501 / 2 = 1750.5 (the remainder is 1, so 2 is not a divisor of 3501)
3501 / 3 = 1167 (the remainder is 0, so 3 is a divisor of 3501)
...
3501 / 3500 = 1.0002857142857 (the remainder is 1, so 3500 is not a divisor of 3501)
3501 / 3501 = 1 (the remainder is 0, so 3501 is a divisor of 3501)

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 3501 (i.e. 59.169248769948). 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 $\frac{N}{d} = D$ )

3501 / 1 = 3501 (the remainder is 0, so 1 and 3501 are divisors of 3501)
3501 / 2 = 1750.5 (the remainder is 1, so 2 is not a divisor of 3501)
3501 / 3 = 1167 (the remainder is 0, so 3 and 1167 are divisors of 3501)
...
3501 / 58 = 60.362068965517 (the remainder is 21, so 58 is not a divisor of 3501)
3501 / 59 = 59.338983050847 (the remainder is 20, so 59 is not a divisor of 3501)