What are the divisors of 892?

1, 2, 4, 223, 446, 892

There is a total of 6 positive divisors.
The sum of these divisors is 1568.
The arithmetic mean is 261.33333333333.

4 even divisors

2, 4, 446, 892

2 odd divisors

1, 223

How to compute the divisors of 892?

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 892 by each of the numbers from 1 to 892 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)

892 / 1 = 892 (the remainder is 0, so 1 is a divisor of 892)
892 / 2 = 446 (the remainder is 0, so 2 is a divisor of 892)
892 / 3 = 297.33333333333 (the remainder is 1, so 3 is not a divisor of 892)
...
892 / 891 = 1.0011223344557 (the remainder is 1, so 891 is not a divisor of 892)
892 / 892 = 1 (the remainder is 0, so 892 is a divisor of 892)

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 892 (i.e. 29.866369046136). 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 $\frac{N}{d} = D$ )

892 / 1 = 892 (the remainder is 0, so 1 and 892 are divisors of 892)
892 / 2 = 446 (the remainder is 0, so 2 and 446 are divisors of 892)
892 / 3 = 297.33333333333 (the remainder is 1, so 3 is not a divisor of 892)
...
892 / 28 = 31.857142857143 (the remainder is 24, so 28 is not a divisor of 892)
892 / 29 = 30.758620689655 (the remainder is 22, so 29 is not a divisor of 892)