What are the divisors of 3334?

1, 2, 1667, 3334

There is a total of 4 positive divisors.
The sum of these divisors is 5004.
The arithmetic mean is 1251.

2 even divisors

2, 3334

2 odd divisors

1, 1667

How to compute the divisors of 3334?

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 3334 by each of the numbers from 1 to 3334 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)

3334 / 1 = 3334 (the remainder is 0, so 1 is a divisor of 3334)
3334 / 2 = 1667 (the remainder is 0, so 2 is a divisor of 3334)
3334 / 3 = 1111.3333333333 (the remainder is 1, so 3 is not a divisor of 3334)
...
3334 / 3333 = 1.000300030003 (the remainder is 1, so 3333 is not a divisor of 3334)
3334 / 3334 = 1 (the remainder is 0, so 3334 is a divisor of 3334)

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 3334 (i.e. 57.740800133008). 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 $\frac{N}{d} = D$ )

3334 / 1 = 3334 (the remainder is 0, so 1 and 3334 are divisors of 3334)
3334 / 2 = 1667 (the remainder is 0, so 2 and 1667 are divisors of 3334)
3334 / 3 = 1111.3333333333 (the remainder is 1, so 3 is not a divisor of 3334)
...
3334 / 56 = 59.535714285714 (the remainder is 30, so 56 is not a divisor of 3334)
3334 / 57 = 58.491228070175 (the remainder is 28, so 57 is not a divisor of 3334)