What are the divisors of 3332?

1, 2, 4, 7, 14, 17, 28, 34, 49, 68, 98, 119, 196, 238, 476, 833, 1666, 3332

There is a total of 18 positive divisors.
The sum of these divisors is 7182.
The arithmetic mean is 399.

12 even divisors

2, 4, 14, 28, 34, 68, 98, 196, 238, 476, 1666, 3332

6 odd divisors

1, 7, 17, 49, 119, 833

How to compute the divisors of 3332?

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 3332 by each of the numbers from 1 to 3332 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)

3332 / 1 = 3332 (the remainder is 0, so 1 is a divisor of 3332)
3332 / 2 = 1666 (the remainder is 0, so 2 is a divisor of 3332)
3332 / 3 = 1110.6666666667 (the remainder is 2, so 3 is not a divisor of 3332)
...
3332 / 3331 = 1.0003002101471 (the remainder is 1, so 3331 is not a divisor of 3332)
3332 / 3332 = 1 (the remainder is 0, so 3332 is a divisor of 3332)

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 3332 (i.e. 57.723478758647). 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 $\frac{N}{d} = D$ )

3332 / 1 = 3332 (the remainder is 0, so 1 and 3332 are divisors of 3332)
3332 / 2 = 1666 (the remainder is 0, so 2 and 1666 are divisors of 3332)
3332 / 3 = 1110.6666666667 (the remainder is 2, so 3 is not a divisor of 3332)
...
3332 / 56 = 59.5 (the remainder is 28, so 56 is not a divisor of 3332)
3332 / 57 = 58.456140350877 (the remainder is 26, so 57 is not a divisor of 3332)