What are the divisors of 1334?

1, 2, 23, 29, 46, 58, 667, 1334

There is a total of 8 positive divisors.
The sum of these divisors is 2160.
The arithmetic mean is 270.

4 even divisors

2, 46, 58, 1334

4 odd divisors

1, 23, 29, 667

How to compute the divisors of 1334?

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 1334 by each of the numbers from 1 to 1334 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)

1334 / 1 = 1334 (the remainder is 0, so 1 is a divisor of 1334)
1334 / 2 = 667 (the remainder is 0, so 2 is a divisor of 1334)
1334 / 3 = 444.66666666667 (the remainder is 2, so 3 is not a divisor of 1334)
...
1334 / 1333 = 1.0007501875469 (the remainder is 1, so 1333 is not a divisor of 1334)
1334 / 1334 = 1 (the remainder is 0, so 1334 is a divisor of 1334)

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 1334 (i.e. 36.523964735499). 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 $\frac{N}{d} = D$ )

1334 / 1 = 1334 (the remainder is 0, so 1 and 1334 are divisors of 1334)
1334 / 2 = 667 (the remainder is 0, so 2 and 667 are divisors of 1334)
1334 / 3 = 444.66666666667 (the remainder is 2, so 3 is not a divisor of 1334)
...
1334 / 35 = 38.114285714286 (the remainder is 4, so 35 is not a divisor of 1334)
1334 / 36 = 37.055555555556 (the remainder is 2, so 36 is not a divisor of 1334)