What are the divisors of 3892?

1, 2, 4, 7, 14, 28, 139, 278, 556, 973, 1946, 3892

There is a total of 12 positive divisors.
The sum of these divisors is 7840.
The arithmetic mean is 653.33333333333.

8 even divisors

2, 4, 14, 28, 278, 556, 1946, 3892

4 odd divisors

1, 7, 139, 973

How to compute the divisors of 3892?

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 3892 by each of the numbers from 1 to 3892 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)

3892 / 1 = 3892 (the remainder is 0, so 1 is a divisor of 3892)
3892 / 2 = 1946 (the remainder is 0, so 2 is a divisor of 3892)
3892 / 3 = 1297.3333333333 (the remainder is 1, so 3 is not a divisor of 3892)
...
3892 / 3891 = 1.000257003341 (the remainder is 1, so 3891 is not a divisor of 3892)
3892 / 3892 = 1 (the remainder is 0, so 3892 is a divisor of 3892)

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 3892 (i.e. 62.385895841929). 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 $\frac{N}{d} = D$ )

3892 / 1 = 3892 (the remainder is 0, so 1 and 3892 are divisors of 3892)
3892 / 2 = 1946 (the remainder is 0, so 2 and 1946 are divisors of 3892)
3892 / 3 = 1297.3333333333 (the remainder is 1, so 3 is not a divisor of 3892)
...
3892 / 61 = 63.803278688525 (the remainder is 49, so 61 is not a divisor of 3892)
3892 / 62 = 62.774193548387 (the remainder is 48, so 62 is not a divisor of 3892)