What are the divisors of 2152?

1, 2, 4, 8, 269, 538, 1076, 2152

There is a total of 8 positive divisors.
The sum of these divisors is 4050.
The arithmetic mean is 506.25.

6 even divisors

2, 4, 8, 538, 1076, 2152

2 odd divisors

1, 269

How to compute the divisors of 2152?

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 2152 by each of the numbers from 1 to 2152 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)

2152 / 1 = 2152 (the remainder is 0, so 1 is a divisor of 2152)
2152 / 2 = 1076 (the remainder is 0, so 2 is a divisor of 2152)
2152 / 3 = 717.33333333333 (the remainder is 1, so 3 is not a divisor of 2152)
...
2152 / 2151 = 1.0004649000465 (the remainder is 1, so 2151 is not a divisor of 2152)
2152 / 2152 = 1 (the remainder is 0, so 2152 is a divisor of 2152)

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 2152 (i.e. 46.389654018973). 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 $\frac{N}{d} = D$ )

2152 / 1 = 2152 (the remainder is 0, so 1 and 2152 are divisors of 2152)
2152 / 2 = 1076 (the remainder is 0, so 2 and 1076 are divisors of 2152)
2152 / 3 = 717.33333333333 (the remainder is 1, so 3 is not a divisor of 2152)
...
2152 / 45 = 47.822222222222 (the remainder is 37, so 45 is not a divisor of 2152)
2152 / 46 = 46.782608695652 (the remainder is 36, so 46 is not a divisor of 2152)