What are the divisors of 2451?

1, 3, 19, 43, 57, 129, 817, 2451

There is a total of 8 positive divisors.
The sum of these divisors is 3520.
The arithmetic mean is 440.

8 odd divisors

1, 3, 19, 43, 57, 129, 817, 2451

How to compute the divisors of 2451?

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 2451 by each of the numbers from 1 to 2451 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)

2451 / 1 = 2451 (the remainder is 0, so 1 is a divisor of 2451)
2451 / 2 = 1225.5 (the remainder is 1, so 2 is not a divisor of 2451)
2451 / 3 = 817 (the remainder is 0, so 3 is a divisor of 2451)
...
2451 / 2450 = 1.0004081632653 (the remainder is 1, so 2450 is not a divisor of 2451)
2451 / 2451 = 1 (the remainder is 0, so 2451 is a divisor of 2451)

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 2451 (i.e. 49.507575177946). 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 $\frac{N}{d} = D$ )

2451 / 1 = 2451 (the remainder is 0, so 1 and 2451 are divisors of 2451)
2451 / 2 = 1225.5 (the remainder is 1, so 2 is not a divisor of 2451)
2451 / 3 = 817 (the remainder is 0, so 3 and 817 are divisors of 2451)
...
2451 / 48 = 51.0625 (the remainder is 3, so 48 is not a divisor of 2451)
2451 / 49 = 50.020408163265 (the remainder is 1, so 49 is not a divisor of 2451)