What are the divisors of 1358?

1, 2, 7, 14, 97, 194, 679, 1358

There is a total of 8 positive divisors.
The sum of these divisors is 2352.
The arithmetic mean is 294.

4 even divisors

2, 14, 194, 1358

4 odd divisors

1, 7, 97, 679

How to compute the divisors of 1358?

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 1358 by each of the numbers from 1 to 1358 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)

1358 / 1 = 1358 (the remainder is 0, so 1 is a divisor of 1358)
1358 / 2 = 679 (the remainder is 0, so 2 is a divisor of 1358)
1358 / 3 = 452.66666666667 (the remainder is 2, so 3 is not a divisor of 1358)
...
1358 / 1357 = 1.0007369196758 (the remainder is 1, so 1357 is not a divisor of 1358)
1358 / 1358 = 1 (the remainder is 0, so 1358 is a divisor of 1358)

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 1358 (i.e. 36.851051545377). 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 $\frac{N}{d} = D$ )

1358 / 1 = 1358 (the remainder is 0, so 1 and 1358 are divisors of 1358)
1358 / 2 = 679 (the remainder is 0, so 2 and 679 are divisors of 1358)
1358 / 3 = 452.66666666667 (the remainder is 2, so 3 is not a divisor of 1358)
...
1358 / 35 = 38.8 (the remainder is 28, so 35 is not a divisor of 1358)
1358 / 36 = 37.722222222222 (the remainder is 26, so 36 is not a divisor of 1358)