What are the divisors of 3506?

1, 2, 1753, 3506

There is a total of 4 positive divisors.
The sum of these divisors is 5262.
The arithmetic mean is 1315.5.

2 even divisors

2, 3506

2 odd divisors

1, 1753

How to compute the divisors of 3506?

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 3506 by each of the numbers from 1 to 3506 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)

3506 / 1 = 3506 (the remainder is 0, so 1 is a divisor of 3506)
3506 / 2 = 1753 (the remainder is 0, so 2 is a divisor of 3506)
3506 / 3 = 1168.6666666667 (the remainder is 2, so 3 is not a divisor of 3506)
...
3506 / 3505 = 1.0002853067047 (the remainder is 1, so 3505 is not a divisor of 3506)
3506 / 3506 = 1 (the remainder is 0, so 3506 is a divisor of 3506)

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 3506 (i.e. 59.21148537235). 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 $\frac{N}{d} = D$ )

3506 / 1 = 3506 (the remainder is 0, so 1 and 3506 are divisors of 3506)
3506 / 2 = 1753 (the remainder is 0, so 2 and 1753 are divisors of 3506)
3506 / 3 = 1168.6666666667 (the remainder is 2, so 3 is not a divisor of 3506)
...
3506 / 58 = 60.448275862069 (the remainder is 26, so 58 is not a divisor of 3506)
3506 / 59 = 59.423728813559 (the remainder is 25, so 59 is not a divisor of 3506)