What are the divisors of 1043?

1, 7, 149, 1043

There is a total of 4 positive divisors.
The sum of these divisors is 1200.
The arithmetic mean is 300.

4 odd divisors

1, 7, 149, 1043

How to compute the divisors of 1043?

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 1043 by each of the numbers from 1 to 1043 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)

1043 / 1 = 1043 (the remainder is 0, so 1 is a divisor of 1043)
1043 / 2 = 521.5 (the remainder is 1, so 2 is not a divisor of 1043)
1043 / 3 = 347.66666666667 (the remainder is 2, so 3 is not a divisor of 1043)
...
1043 / 1042 = 1.0009596928983 (the remainder is 1, so 1042 is not a divisor of 1043)
1043 / 1043 = 1 (the remainder is 0, so 1043 is a divisor of 1043)

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 1043 (i.e. 32.29551052391). 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 $\frac{N}{d} = D$ )

1043 / 1 = 1043 (the remainder is 0, so 1 and 1043 are divisors of 1043)
1043 / 2 = 521.5 (the remainder is 1, so 2 is not a divisor of 1043)
1043 / 3 = 347.66666666667 (the remainder is 2, so 3 is not a divisor of 1043)
...
1043 / 31 = 33.645161290323 (the remainder is 20, so 31 is not a divisor of 1043)
1043 / 32 = 32.59375 (the remainder is 19, so 32 is not a divisor of 1043)