What are the divisors of 1573?

1, 11, 13, 121, 143, 1573

There is a total of 6 positive divisors.
The sum of these divisors is 1862.
The arithmetic mean is 310.33333333333.

6 odd divisors

1, 11, 13, 121, 143, 1573

How to compute the divisors of 1573?

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 1573 by each of the numbers from 1 to 1573 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)

1573 / 1 = 1573 (the remainder is 0, so 1 is a divisor of 1573)
1573 / 2 = 786.5 (the remainder is 1, so 2 is not a divisor of 1573)
1573 / 3 = 524.33333333333 (the remainder is 1, so 3 is not a divisor of 1573)
...
1573 / 1572 = 1.0006361323155 (the remainder is 1, so 1572 is not a divisor of 1573)
1573 / 1573 = 1 (the remainder is 0, so 1573 is a divisor of 1573)

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 1573 (i.e. 39.661064030104). 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 $\frac{N}{d} = D$ )

1573 / 1 = 1573 (the remainder is 0, so 1 and 1573 are divisors of 1573)
1573 / 2 = 786.5 (the remainder is 1, so 2 is not a divisor of 1573)
1573 / 3 = 524.33333333333 (the remainder is 1, so 3 is not a divisor of 1573)
...
1573 / 38 = 41.394736842105 (the remainder is 15, so 38 is not a divisor of 1573)
1573 / 39 = 40.333333333333 (the remainder is 13, so 39 is not a divisor of 1573)