What are the divisors of 1330?

1, 2, 5, 7, 10, 14, 19, 35, 38, 70, 95, 133, 190, 266, 665, 1330

There is a total of 16 positive divisors.
The sum of these divisors is 2880.
The arithmetic mean is 180.

8 even divisors

2, 10, 14, 38, 70, 190, 266, 1330

8 odd divisors

1, 5, 7, 19, 35, 95, 133, 665

How to compute the divisors of 1330?

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 1330 by each of the numbers from 1 to 1330 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)

1330 / 1 = 1330 (the remainder is 0, so 1 is a divisor of 1330)
1330 / 2 = 665 (the remainder is 0, so 2 is a divisor of 1330)
1330 / 3 = 443.33333333333 (the remainder is 1, so 3 is not a divisor of 1330)
...
1330 / 1329 = 1.0007524454477 (the remainder is 1, so 1329 is not a divisor of 1330)
1330 / 1330 = 1 (the remainder is 0, so 1330 is a divisor of 1330)

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 1330 (i.e. 36.469165057621). 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 $\frac{N}{d} = D$ )

1330 / 1 = 1330 (the remainder is 0, so 1 and 1330 are divisors of 1330)
1330 / 2 = 665 (the remainder is 0, so 2 and 665 are divisors of 1330)
1330 / 3 = 443.33333333333 (the remainder is 1, so 3 is not a divisor of 1330)
...
1330 / 35 = 38 (the remainder is 0, so 35 and 38 are divisors of 1330)
1330 / 36 = 36.944444444444 (the remainder is 34, so 36 is not a divisor of 1330)