What are the divisors of 1041?

1, 3, 347, 1041

There is a total of 4 positive divisors.
The sum of these divisors is 1392.
The arithmetic mean is 348.

4 odd divisors

1, 3, 347, 1041

How to compute the divisors of 1041?

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 1041 by each of the numbers from 1 to 1041 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)

1041 / 1 = 1041 (the remainder is 0, so 1 is a divisor of 1041)
1041 / 2 = 520.5 (the remainder is 1, so 2 is not a divisor of 1041)
1041 / 3 = 347 (the remainder is 0, so 3 is a divisor of 1041)
...
1041 / 1040 = 1.0009615384615 (the remainder is 1, so 1040 is not a divisor of 1041)
1041 / 1041 = 1 (the remainder is 0, so 1041 is a divisor of 1041)

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 1041 (i.e. 32.264531609803). 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 $\frac{N}{d} = D$ )

1041 / 1 = 1041 (the remainder is 0, so 1 and 1041 are divisors of 1041)
1041 / 2 = 520.5 (the remainder is 1, so 2 is not a divisor of 1041)
1041 / 3 = 347 (the remainder is 0, so 3 and 347 are divisors of 1041)
...
1041 / 31 = 33.58064516129 (the remainder is 18, so 31 is not a divisor of 1041)
1041 / 32 = 32.53125 (the remainder is 17, so 32 is not a divisor of 1041)