What are the divisors of 1037?

1, 17, 61, 1037

There is a total of 4 positive divisors.
The sum of these divisors is 1116.
The arithmetic mean is 279.

4 odd divisors

1, 17, 61, 1037

How to compute the divisors of 1037?

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 1037 by each of the numbers from 1 to 1037 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)

1037 / 1 = 1037 (the remainder is 0, so 1 is a divisor of 1037)
1037 / 2 = 518.5 (the remainder is 1, so 2 is not a divisor of 1037)
1037 / 3 = 345.66666666667 (the remainder is 2, so 3 is not a divisor of 1037)
...
1037 / 1036 = 1.0009652509653 (the remainder is 1, so 1036 is not a divisor of 1037)
1037 / 1037 = 1 (the remainder is 0, so 1037 is a divisor of 1037)

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 1037 (i.e. 32.202484376209). 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 $\frac{N}{d} = D$ )

1037 / 1 = 1037 (the remainder is 0, so 1 and 1037 are divisors of 1037)
1037 / 2 = 518.5 (the remainder is 1, so 2 is not a divisor of 1037)
1037 / 3 = 345.66666666667 (the remainder is 2, so 3 is not a divisor of 1037)
...
1037 / 31 = 33.451612903226 (the remainder is 14, so 31 is not a divisor of 1037)
1037 / 32 = 32.40625 (the remainder is 13, so 32 is not a divisor of 1037)