What are the divisors of 897?

1, 3, 13, 23, 39, 69, 299, 897

There is a total of 8 positive divisors.
The sum of these divisors is 1344.
The arithmetic mean is 168.

8 odd divisors

1, 3, 13, 23, 39, 69, 299, 897

How to compute the divisors of 897?

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 897 by each of the numbers from 1 to 897 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)

897 / 1 = 897 (the remainder is 0, so 1 is a divisor of 897)
897 / 2 = 448.5 (the remainder is 1, so 2 is not a divisor of 897)
897 / 3 = 299 (the remainder is 0, so 3 is a divisor of 897)
...
897 / 896 = 1.0011160714286 (the remainder is 1, so 896 is not a divisor of 897)
897 / 897 = 1 (the remainder is 0, so 897 is a divisor of 897)

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 897 (i.e. 29.949958263744). 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 $\frac{N}{d} = D$ )

897 / 1 = 897 (the remainder is 0, so 1 and 897 are divisors of 897)
897 / 2 = 448.5 (the remainder is 1, so 2 is not a divisor of 897)
897 / 3 = 299 (the remainder is 0, so 3 and 299 are divisors of 897)
...
897 / 28 = 32.035714285714 (the remainder is 1, so 28 is not a divisor of 897)
897 / 29 = 30.931034482759 (the remainder is 27, so 29 is not a divisor of 897)