What are the divisors of 2153?

1, 2153

There is a total of 2 positive divisors.
The sum of these divisors is 2154.
The arithmetic mean is 1077.

2 odd divisors

1, 2153

How to compute the divisors of 2153?

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 2153 by each of the numbers from 1 to 2153 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)

2153 / 1 = 2153 (the remainder is 0, so 1 is a divisor of 2153)
2153 / 2 = 1076.5 (the remainder is 1, so 2 is not a divisor of 2153)
2153 / 3 = 717.66666666667 (the remainder is 2, so 3 is not a divisor of 2153)
...
2153 / 2152 = 1.0004646840149 (the remainder is 1, so 2152 is not a divisor of 2153)
2153 / 2153 = 1 (the remainder is 0, so 2153 is a divisor of 2153)

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 2153 (i.e. 46.400431032481). 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 $\frac{N}{d} = D$ )

2153 / 1 = 2153 (the remainder is 0, so 1 and 2153 are divisors of 2153)
2153 / 2 = 1076.5 (the remainder is 1, so 2 is not a divisor of 2153)
2153 / 3 = 717.66666666667 (the remainder is 2, so 3 is not a divisor of 2153)
...
2153 / 45 = 47.844444444444 (the remainder is 38, so 45 is not a divisor of 2153)
2153 / 46 = 46.804347826087 (the remainder is 37, so 46 is not a divisor of 2153)