What are the divisors of 1052?

1, 2, 4, 263, 526, 1052

There is a total of 6 positive divisors.
The sum of these divisors is 1848.
The arithmetic mean is 308.

4 even divisors

2, 4, 526, 1052

2 odd divisors

1, 263

How to compute the divisors of 1052?

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 1052 by each of the numbers from 1 to 1052 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)

1052 / 1 = 1052 (the remainder is 0, so 1 is a divisor of 1052)
1052 / 2 = 526 (the remainder is 0, so 2 is a divisor of 1052)
1052 / 3 = 350.66666666667 (the remainder is 2, so 3 is not a divisor of 1052)
...
1052 / 1051 = 1.0009514747859 (the remainder is 1, so 1051 is not a divisor of 1052)
1052 / 1052 = 1 (the remainder is 0, so 1052 is a divisor of 1052)

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 1052 (i.e. 32.434549480454). 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 $\frac{N}{d} = D$ )

1052 / 1 = 1052 (the remainder is 0, so 1 and 1052 are divisors of 1052)
1052 / 2 = 526 (the remainder is 0, so 2 and 526 are divisors of 1052)
1052 / 3 = 350.66666666667 (the remainder is 2, so 3 is not a divisor of 1052)
...
1052 / 31 = 33.935483870968 (the remainder is 29, so 31 is not a divisor of 1052)
1052 / 32 = 32.875 (the remainder is 28, so 32 is not a divisor of 1052)