What are the divisors of 1046?

1, 2, 523, 1046

There is a total of 4 positive divisors.
The sum of these divisors is 1572.
The arithmetic mean is 393.

2 even divisors

2, 1046

2 odd divisors

1, 523

How to compute the divisors of 1046?

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 1046 by each of the numbers from 1 to 1046 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)

1046 / 1 = 1046 (the remainder is 0, so 1 is a divisor of 1046)
1046 / 2 = 523 (the remainder is 0, so 2 is a divisor of 1046)
1046 / 3 = 348.66666666667 (the remainder is 2, so 3 is not a divisor of 1046)
...
1046 / 1045 = 1.000956937799 (the remainder is 1, so 1045 is not a divisor of 1046)
1046 / 1046 = 1 (the remainder is 0, so 1046 is a divisor of 1046)

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 1046 (i.e. 32.341923257592). 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 $\frac{N}{d} = D$ )

1046 / 1 = 1046 (the remainder is 0, so 1 and 1046 are divisors of 1046)
1046 / 2 = 523 (the remainder is 0, so 2 and 523 are divisors of 1046)
1046 / 3 = 348.66666666667 (the remainder is 2, so 3 is not a divisor of 1046)
...
1046 / 31 = 33.741935483871 (the remainder is 23, so 31 is not a divisor of 1046)
1046 / 32 = 32.6875 (the remainder is 22, so 32 is not a divisor of 1046)