What are the divisors of 3551?

1, 53, 67, 3551

There is a total of 4 positive divisors.
The sum of these divisors is 3672.
The arithmetic mean is 918.

4 odd divisors

1, 53, 67, 3551

How to compute the divisors of 3551?

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 3551 by each of the numbers from 1 to 3551 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)

3551 / 1 = 3551 (the remainder is 0, so 1 is a divisor of 3551)
3551 / 2 = 1775.5 (the remainder is 1, so 2 is not a divisor of 3551)
3551 / 3 = 1183.6666666667 (the remainder is 2, so 3 is not a divisor of 3551)
...
3551 / 3550 = 1.0002816901408 (the remainder is 1, so 3550 is not a divisor of 3551)
3551 / 3551 = 1 (the remainder is 0, so 3551 is a divisor of 3551)

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 3551 (i.e. 59.590267661758). 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 $\frac{N}{d} = D$ )

3551 / 1 = 3551 (the remainder is 0, so 1 and 3551 are divisors of 3551)
3551 / 2 = 1775.5 (the remainder is 1, so 2 is not a divisor of 3551)
3551 / 3 = 1183.6666666667 (the remainder is 2, so 3 is not a divisor of 3551)
...
3551 / 58 = 61.224137931034 (the remainder is 13, so 58 is not a divisor of 3551)
3551 / 59 = 60.186440677966 (the remainder is 11, so 59 is not a divisor of 3551)