What are the divisors of 1042?

1, 2, 521, 1042

There is a total of 4 positive divisors.
The sum of these divisors is 1566.
The arithmetic mean is 391.5.

2 even divisors

2, 1042

2 odd divisors

1, 521

How to compute the divisors of 1042?

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 1042 by each of the numbers from 1 to 1042 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)

1042 / 1 = 1042 (the remainder is 0, so 1 is a divisor of 1042)
1042 / 2 = 521 (the remainder is 0, so 2 is a divisor of 1042)
1042 / 3 = 347.33333333333 (the remainder is 1, so 3 is not a divisor of 1042)
...
1042 / 1041 = 1.0009606147935 (the remainder is 1, so 1041 is not a divisor of 1042)
1042 / 1042 = 1 (the remainder is 0, so 1042 is a divisor of 1042)

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 1042 (i.e. 32.280024783138). 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 $\frac{N}{d} = D$ )

1042 / 1 = 1042 (the remainder is 0, so 1 and 1042 are divisors of 1042)
1042 / 2 = 521 (the remainder is 0, so 2 and 521 are divisors of 1042)
1042 / 3 = 347.33333333333 (the remainder is 1, so 3 is not a divisor of 1042)
...
1042 / 31 = 33.612903225806 (the remainder is 19, so 31 is not a divisor of 1042)
1042 / 32 = 32.5625 (the remainder is 18, so 32 is not a divisor of 1042)