What are the divisors of 3573?

1, 3, 9, 397, 1191, 3573

There is a total of 6 positive divisors.
The sum of these divisors is 5174.
The arithmetic mean is 862.33333333333.

6 odd divisors

1, 3, 9, 397, 1191, 3573

How to compute the divisors of 3573?

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 3573 by each of the numbers from 1 to 3573 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)

3573 / 1 = 3573 (the remainder is 0, so 1 is a divisor of 3573)
3573 / 2 = 1786.5 (the remainder is 1, so 2 is not a divisor of 3573)
3573 / 3 = 1191 (the remainder is 0, so 3 is a divisor of 3573)
...
3573 / 3572 = 1.0002799552072 (the remainder is 1, so 3572 is not a divisor of 3573)
3573 / 3573 = 1 (the remainder is 0, so 3573 is a divisor of 3573)

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 3573 (i.e. 59.774576535514). 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 $\frac{N}{d} = D$ )

3573 / 1 = 3573 (the remainder is 0, so 1 and 3573 are divisors of 3573)
3573 / 2 = 1786.5 (the remainder is 1, so 2 is not a divisor of 3573)
3573 / 3 = 1191 (the remainder is 0, so 3 and 1191 are divisors of 3573)
...
3573 / 58 = 61.603448275862 (the remainder is 35, so 58 is not a divisor of 3573)
3573 / 59 = 60.559322033898 (the remainder is 33, so 59 is not a divisor of 3573)