What are the divisors of 3392?

1, 2, 4, 8, 16, 32, 53, 64, 106, 212, 424, 848, 1696, 3392

There is a total of 14 positive divisors.
The sum of these divisors is 6858.
The arithmetic mean is 489.85714285714.

12 even divisors

2, 4, 8, 16, 32, 64, 106, 212, 424, 848, 1696, 3392

2 odd divisors

1, 53

How to compute the divisors of 3392?

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 3392 by each of the numbers from 1 to 3392 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)

3392 / 1 = 3392 (the remainder is 0, so 1 is a divisor of 3392)
3392 / 2 = 1696 (the remainder is 0, so 2 is a divisor of 3392)
3392 / 3 = 1130.6666666667 (the remainder is 2, so 3 is not a divisor of 3392)
...
3392 / 3391 = 1.0002948982601 (the remainder is 1, so 3391 is not a divisor of 3392)
3392 / 3392 = 1 (the remainder is 0, so 3392 is a divisor of 3392)

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 3392 (i.e. 58.240879114244). 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 $\frac{N}{d} = D$ )

3392 / 1 = 3392 (the remainder is 0, so 1 and 3392 are divisors of 3392)
3392 / 2 = 1696 (the remainder is 0, so 2 and 1696 are divisors of 3392)
3392 / 3 = 1130.6666666667 (the remainder is 2, so 3 is not a divisor of 3392)
...
3392 / 57 = 59.508771929825 (the remainder is 29, so 57 is not a divisor of 3392)
3392 / 58 = 58.48275862069 (the remainder is 28, so 58 is not a divisor of 3392)