What are the divisors of 3345?

1, 3, 5, 15, 223, 669, 1115, 3345

There is a total of 8 positive divisors.
The sum of these divisors is 5376.
The arithmetic mean is 672.

8 odd divisors

1, 3, 5, 15, 223, 669, 1115, 3345

How to compute the divisors of 3345?

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 3345 by each of the numbers from 1 to 3345 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)

3345 / 1 = 3345 (the remainder is 0, so 1 is a divisor of 3345)
3345 / 2 = 1672.5 (the remainder is 1, so 2 is not a divisor of 3345)
3345 / 3 = 1115 (the remainder is 0, so 3 is a divisor of 3345)
...
3345 / 3344 = 1.0002990430622 (the remainder is 1, so 3344 is not a divisor of 3345)
3345 / 3345 = 1 (the remainder is 0, so 3345 is a divisor of 3345)

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 3345 (i.e. 57.835974963685). 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 $\frac{N}{d} = D$ )

3345 / 1 = 3345 (the remainder is 0, so 1 and 3345 are divisors of 3345)
3345 / 2 = 1672.5 (the remainder is 1, so 2 is not a divisor of 3345)
3345 / 3 = 1115 (the remainder is 0, so 3 and 1115 are divisors of 3345)
...
3345 / 56 = 59.732142857143 (the remainder is 41, so 56 is not a divisor of 3345)
3345 / 57 = 58.684210526316 (the remainder is 39, so 57 is not a divisor of 3345)