What are the divisors of 2132?

1, 2, 4, 13, 26, 41, 52, 82, 164, 533, 1066, 2132

There is a total of 12 positive divisors.
The sum of these divisors is 4116.
The arithmetic mean is 343.

8 even divisors

2, 4, 26, 52, 82, 164, 1066, 2132

4 odd divisors

1, 13, 41, 533

How to compute the divisors of 2132?

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 2132 by each of the numbers from 1 to 2132 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)

2132 / 1 = 2132 (the remainder is 0, so 1 is a divisor of 2132)
2132 / 2 = 1066 (the remainder is 0, so 2 is a divisor of 2132)
2132 / 3 = 710.66666666667 (the remainder is 2, so 3 is not a divisor of 2132)
...
2132 / 2131 = 1.0004692632567 (the remainder is 1, so 2131 is not a divisor of 2132)
2132 / 2132 = 1 (the remainder is 0, so 2132 is a divisor of 2132)

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 2132 (i.e. 46.173585522461). 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 $\frac{N}{d} = D$ )

2132 / 1 = 2132 (the remainder is 0, so 1 and 2132 are divisors of 2132)
2132 / 2 = 1066 (the remainder is 0, so 2 and 1066 are divisors of 2132)
2132 / 3 = 710.66666666667 (the remainder is 2, so 3 is not a divisor of 2132)
...
2132 / 45 = 47.377777777778 (the remainder is 17, so 45 is not a divisor of 2132)
2132 / 46 = 46.347826086957 (the remainder is 16, so 46 is not a divisor of 2132)