What are the divisors of 6132?

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 73, 84, 146, 219, 292, 438, 511, 876, 1022, 1533, 2044, 3066, 6132

There is a total of 24 positive divisors.
The sum of these divisors is 16576.
The arithmetic mean is 690.66666666667.

16 even divisors

2, 4, 6, 12, 14, 28, 42, 84, 146, 292, 438, 876, 1022, 2044, 3066, 6132

8 odd divisors

1, 3, 7, 21, 73, 219, 511, 1533

How to compute the divisors of 6132?

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 6132 by each of the numbers from 1 to 6132 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)

6132 / 1 = 6132 (the remainder is 0, so 1 is a divisor of 6132)
6132 / 2 = 3066 (the remainder is 0, so 2 is a divisor of 6132)
6132 / 3 = 2044 (the remainder is 0, so 3 is a divisor of 6132)
...
6132 / 6131 = 1.0001631055293 (the remainder is 1, so 6131 is not a divisor of 6132)
6132 / 6132 = 1 (the remainder is 0, so 6132 is a divisor of 6132)

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 6132 (i.e. 78.307087801808). 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 $\frac{N}{d} = D$ )

6132 / 1 = 6132 (the remainder is 0, so 1 and 6132 are divisors of 6132)
6132 / 2 = 3066 (the remainder is 0, so 2 and 3066 are divisors of 6132)
6132 / 3 = 2044 (the remainder is 0, so 3 and 2044 are divisors of 6132)
...
6132 / 77 = 79.636363636364 (the remainder is 49, so 77 is not a divisor of 6132)
6132 / 78 = 78.615384615385 (the remainder is 48, so 78 is not a divisor of 6132)