What are the divisors of 6052?

1, 2, 4, 17, 34, 68, 89, 178, 356, 1513, 3026, 6052

There is a total of 12 positive divisors.
The sum of these divisors is 11340.
The arithmetic mean is 945.

8 even divisors

2, 4, 34, 68, 178, 356, 3026, 6052

4 odd divisors

1, 17, 89, 1513

How to compute the divisors of 6052?

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 6052 by each of the numbers from 1 to 6052 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)

6052 / 1 = 6052 (the remainder is 0, so 1 is a divisor of 6052)
6052 / 2 = 3026 (the remainder is 0, so 2 is a divisor of 6052)
6052 / 3 = 2017.3333333333 (the remainder is 1, so 3 is not a divisor of 6052)
...
6052 / 6051 = 1.0001652619402 (the remainder is 1, so 6051 is not a divisor of 6052)
6052 / 6052 = 1 (the remainder is 0, so 6052 is a divisor of 6052)

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 6052 (i.e. 77.794601355107). 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 $\frac{N}{d} = D$ )

6052 / 1 = 6052 (the remainder is 0, so 1 and 6052 are divisors of 6052)
6052 / 2 = 3026 (the remainder is 0, so 2 and 3026 are divisors of 6052)
6052 / 3 = 2017.3333333333 (the remainder is 1, so 3 is not a divisor of 6052)
...
6052 / 76 = 79.631578947368 (the remainder is 48, so 76 is not a divisor of 6052)
6052 / 77 = 78.597402597403 (the remainder is 46, so 77 is not a divisor of 6052)