What are the divisors of 3496?

1, 2, 4, 8, 19, 23, 38, 46, 76, 92, 152, 184, 437, 874, 1748, 3496

There is a total of 16 positive divisors.
The sum of these divisors is 7200.
The arithmetic mean is 450.

12 even divisors

2, 4, 8, 38, 46, 76, 92, 152, 184, 874, 1748, 3496

4 odd divisors

1, 19, 23, 437

How to compute the divisors of 3496?

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 3496 by each of the numbers from 1 to 3496 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)

3496 / 1 = 3496 (the remainder is 0, so 1 is a divisor of 3496)
3496 / 2 = 1748 (the remainder is 0, so 2 is a divisor of 3496)
3496 / 3 = 1165.3333333333 (the remainder is 1, so 3 is not a divisor of 3496)
...
3496 / 3495 = 1.0002861230329 (the remainder is 1, so 3495 is not a divisor of 3496)
3496 / 3496 = 1 (the remainder is 0, so 3496 is a divisor of 3496)

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 3496 (i.e. 59.126981996378). 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 $\frac{N}{d} = D$ )

3496 / 1 = 3496 (the remainder is 0, so 1 and 3496 are divisors of 3496)
3496 / 2 = 1748 (the remainder is 0, so 2 and 1748 are divisors of 3496)
3496 / 3 = 1165.3333333333 (the remainder is 1, so 3 is not a divisor of 3496)
...
3496 / 58 = 60.275862068966 (the remainder is 16, so 58 is not a divisor of 3496)
3496 / 59 = 59.254237288136 (the remainder is 15, so 59 is not a divisor of 3496)