What are the divisors of 2553?

1, 3, 23, 37, 69, 111, 851, 2553

There is a total of 8 positive divisors.
The sum of these divisors is 3648.
The arithmetic mean is 456.

8 odd divisors

1, 3, 23, 37, 69, 111, 851, 2553

How to compute the divisors of 2553?

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 2553 by each of the numbers from 1 to 2553 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)

2553 / 1 = 2553 (the remainder is 0, so 1 is a divisor of 2553)
2553 / 2 = 1276.5 (the remainder is 1, so 2 is not a divisor of 2553)
2553 / 3 = 851 (the remainder is 0, so 3 is a divisor of 2553)
...
2553 / 2552 = 1.0003918495298 (the remainder is 1, so 2552 is not a divisor of 2553)
2553 / 2553 = 1 (the remainder is 0, so 2553 is a divisor of 2553)

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 2553 (i.e. 50.527220386639). 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 $\frac{N}{d} = D$ )

2553 / 1 = 2553 (the remainder is 0, so 1 and 2553 are divisors of 2553)
2553 / 2 = 1276.5 (the remainder is 1, so 2 is not a divisor of 2553)
2553 / 3 = 851 (the remainder is 0, so 3 and 851 are divisors of 2553)
...
2553 / 49 = 52.102040816327 (the remainder is 5, so 49 is not a divisor of 2553)
2553 / 50 = 51.06 (the remainder is 3, so 50 is not a divisor of 2553)