What are the divisors of 551?

1, 19, 29, 551

There is a total of 4 positive divisors.
The sum of these divisors is 600.
The arithmetic mean is 150.

4 odd divisors

1, 19, 29, 551

How to compute the divisors of 551?

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 551 by each of the numbers from 1 to 551 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)

551 / 1 = 551 (the remainder is 0, so 1 is a divisor of 551)
551 / 2 = 275.5 (the remainder is 1, so 2 is not a divisor of 551)
551 / 3 = 183.66666666667 (the remainder is 2, so 3 is not a divisor of 551)
...
551 / 550 = 1.0018181818182 (the remainder is 1, so 550 is not a divisor of 551)
551 / 551 = 1 (the remainder is 0, so 551 is a divisor of 551)

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 551 (i.e. 23.473389188611). 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 $\frac{N}{d} = D$ )

551 / 1 = 551 (the remainder is 0, so 1 and 551 are divisors of 551)
551 / 2 = 275.5 (the remainder is 1, so 2 is not a divisor of 551)
551 / 3 = 183.66666666667 (the remainder is 2, so 3 is not a divisor of 551)
...
551 / 22 = 25.045454545455 (the remainder is 1, so 22 is not a divisor of 551)
551 / 23 = 23.95652173913 (the remainder is 22, so 23 is not a divisor of 551)