What are the divisors of 1146?

1, 2, 3, 6, 191, 382, 573, 1146

There is a total of 8 positive divisors.
The sum of these divisors is 2304.
The arithmetic mean is 288.

4 even divisors

2, 6, 382, 1146

4 odd divisors

1, 3, 191, 573

How to compute the divisors of 1146?

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 1146 by each of the numbers from 1 to 1146 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)

1146 / 1 = 1146 (the remainder is 0, so 1 is a divisor of 1146)
1146 / 2 = 573 (the remainder is 0, so 2 is a divisor of 1146)
1146 / 3 = 382 (the remainder is 0, so 3 is a divisor of 1146)
...
1146 / 1145 = 1.0008733624454 (the remainder is 1, so 1145 is not a divisor of 1146)
1146 / 1146 = 1 (the remainder is 0, so 1146 is a divisor of 1146)

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 1146 (i.e. 33.852621759622). 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 $\frac{N}{d} = D$ )

1146 / 1 = 1146 (the remainder is 0, so 1 and 1146 are divisors of 1146)
1146 / 2 = 573 (the remainder is 0, so 2 and 573 are divisors of 1146)
1146 / 3 = 382 (the remainder is 0, so 3 and 382 are divisors of 1146)
...
1146 / 32 = 35.8125 (the remainder is 26, so 32 is not a divisor of 1146)
1146 / 33 = 34.727272727273 (the remainder is 24, so 33 is not a divisor of 1146)