What are the divisors of 1551?

1, 3, 11, 33, 47, 141, 517, 1551

There is a total of 8 positive divisors.
The sum of these divisors is 2304.
The arithmetic mean is 288.

8 odd divisors

1, 3, 11, 33, 47, 141, 517, 1551

How to compute the divisors of 1551?

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 1551 by each of the numbers from 1 to 1551 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)

1551 / 1 = 1551 (the remainder is 0, so 1 is a divisor of 1551)
1551 / 2 = 775.5 (the remainder is 1, so 2 is not a divisor of 1551)
1551 / 3 = 517 (the remainder is 0, so 3 is a divisor of 1551)
...
1551 / 1550 = 1.0006451612903 (the remainder is 1, so 1550 is not a divisor of 1551)
1551 / 1551 = 1 (the remainder is 0, so 1551 is a divisor of 1551)

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 1551 (i.e. 39.38273733503). 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 $\frac{N}{d} = D$ )

1551 / 1 = 1551 (the remainder is 0, so 1 and 1551 are divisors of 1551)
1551 / 2 = 775.5 (the remainder is 1, so 2 is not a divisor of 1551)
1551 / 3 = 517 (the remainder is 0, so 3 and 517 are divisors of 1551)
...
1551 / 38 = 40.815789473684 (the remainder is 31, so 38 is not a divisor of 1551)
1551 / 39 = 39.769230769231 (the remainder is 30, so 39 is not a divisor of 1551)