What are the divisors of 894?

1, 2, 3, 6, 149, 298, 447, 894

There is a total of 8 positive divisors.
The sum of these divisors is 1800.
The arithmetic mean is 225.

4 even divisors

2, 6, 298, 894

4 odd divisors

1, 3, 149, 447

How to compute the divisors of 894?

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 894 by each of the numbers from 1 to 894 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)

894 / 1 = 894 (the remainder is 0, so 1 is a divisor of 894)
894 / 2 = 447 (the remainder is 0, so 2 is a divisor of 894)
894 / 3 = 298 (the remainder is 0, so 3 is a divisor of 894)
...
894 / 893 = 1.0011198208287 (the remainder is 1, so 893 is not a divisor of 894)
894 / 894 = 1 (the remainder is 0, so 894 is a divisor of 894)

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 894 (i.e. 29.899832775452). 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 $\frac{N}{d} = D$ )

894 / 1 = 894 (the remainder is 0, so 1 and 894 are divisors of 894)
894 / 2 = 447 (the remainder is 0, so 2 and 447 are divisors of 894)
894 / 3 = 298 (the remainder is 0, so 3 and 298 are divisors of 894)
...
894 / 28 = 31.928571428571 (the remainder is 26, so 28 is not a divisor of 894)
894 / 29 = 30.827586206897 (the remainder is 24, so 29 is not a divisor of 894)