What are the divisors of 898?

1, 2, 449, 898

There is a total of 4 positive divisors.
The sum of these divisors is 1350.
The arithmetic mean is 337.5.

2 even divisors

2, 898

2 odd divisors

1, 449

How to compute the divisors of 898?

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 898 by each of the numbers from 1 to 898 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)

898 / 1 = 898 (the remainder is 0, so 1 is a divisor of 898)
898 / 2 = 449 (the remainder is 0, so 2 is a divisor of 898)
898 / 3 = 299.33333333333 (the remainder is 1, so 3 is not a divisor of 898)
...
898 / 897 = 1.0011148272018 (the remainder is 1, so 897 is not a divisor of 898)
898 / 898 = 1 (the remainder is 0, so 898 is a divisor of 898)

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 898 (i.e. 29.966648127543). 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 $\frac{N}{d} = D$ )

898 / 1 = 898 (the remainder is 0, so 1 and 898 are divisors of 898)
898 / 2 = 449 (the remainder is 0, so 2 and 449 are divisors of 898)
898 / 3 = 299.33333333333 (the remainder is 1, so 3 is not a divisor of 898)
...
898 / 28 = 32.071428571429 (the remainder is 2, so 28 is not a divisor of 898)
898 / 29 = 30.965517241379 (the remainder is 28, so 29 is not a divisor of 898)