What are the divisors of 3692?

1, 2, 4, 13, 26, 52, 71, 142, 284, 923, 1846, 3692

There is a total of 12 positive divisors.
The sum of these divisors is 7056.
The arithmetic mean is 588.

8 even divisors

2, 4, 26, 52, 142, 284, 1846, 3692

4 odd divisors

1, 13, 71, 923

How to compute the divisors of 3692?

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 3692 by each of the numbers from 1 to 3692 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)

3692 / 1 = 3692 (the remainder is 0, so 1 is a divisor of 3692)
3692 / 2 = 1846 (the remainder is 0, so 2 is a divisor of 3692)
3692 / 3 = 1230.6666666667 (the remainder is 2, so 3 is not a divisor of 3692)
...
3692 / 3691 = 1.0002709292875 (the remainder is 1, so 3691 is not a divisor of 3692)
3692 / 3692 = 1 (the remainder is 0, so 3692 is a divisor of 3692)

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 3692 (i.e. 60.761830123853). 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 $\frac{N}{d} = D$ )

3692 / 1 = 3692 (the remainder is 0, so 1 and 3692 are divisors of 3692)
3692 / 2 = 1846 (the remainder is 0, so 2 and 1846 are divisors of 3692)
3692 / 3 = 1230.6666666667 (the remainder is 2, so 3 is not a divisor of 3692)
...
3692 / 59 = 62.576271186441 (the remainder is 34, so 59 is not a divisor of 3692)
3692 / 60 = 61.533333333333 (the remainder is 32, so 60 is not a divisor of 3692)