What are the divisors of 4052?

1, 2, 4, 1013, 2026, 4052

There is a total of 6 positive divisors.
The sum of these divisors is 7098.
The arithmetic mean is 1183.

4 even divisors

2, 4, 2026, 4052

2 odd divisors

1, 1013

How to compute the divisors of 4052?

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 4052 by each of the numbers from 1 to 4052 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)

4052 / 1 = 4052 (the remainder is 0, so 1 is a divisor of 4052)
4052 / 2 = 2026 (the remainder is 0, so 2 is a divisor of 4052)
4052 / 3 = 1350.6666666667 (the remainder is 2, so 3 is not a divisor of 4052)
...
4052 / 4051 = 1.000246852629 (the remainder is 1, so 4051 is not a divisor of 4052)
4052 / 4052 = 1 (the remainder is 0, so 4052 is a divisor of 4052)

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 4052 (i.e. 63.655321851358). 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 $\frac{N}{d} = D$ )

4052 / 1 = 4052 (the remainder is 0, so 1 and 4052 are divisors of 4052)
4052 / 2 = 2026 (the remainder is 0, so 2 and 2026 are divisors of 4052)
4052 / 3 = 1350.6666666667 (the remainder is 2, so 3 is not a divisor of 4052)
...
4052 / 62 = 65.354838709677 (the remainder is 22, so 62 is not a divisor of 4052)
4052 / 63 = 64.31746031746 (the remainder is 20, so 63 is not a divisor of 4052)