What are the divisors of 3377?

1, 11, 307, 3377

There is a total of 4 positive divisors.
The sum of these divisors is 3696.
The arithmetic mean is 924.

4 odd divisors

1, 11, 307, 3377

How to compute the divisors of 3377?

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 3377 by each of the numbers from 1 to 3377 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)

3377 / 1 = 3377 (the remainder is 0, so 1 is a divisor of 3377)
3377 / 2 = 1688.5 (the remainder is 1, so 2 is not a divisor of 3377)
3377 / 3 = 1125.6666666667 (the remainder is 2, so 3 is not a divisor of 3377)
...
3377 / 3376 = 1.0002962085308 (the remainder is 1, so 3376 is not a divisor of 3377)
3377 / 3377 = 1 (the remainder is 0, so 3377 is a divisor of 3377)

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 3377 (i.e. 58.111960903071). 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 $\frac{N}{d} = D$ )

3377 / 1 = 3377 (the remainder is 0, so 1 and 3377 are divisors of 3377)
3377 / 2 = 1688.5 (the remainder is 1, so 2 is not a divisor of 3377)
3377 / 3 = 1125.6666666667 (the remainder is 2, so 3 is not a divisor of 3377)
...
3377 / 57 = 59.245614035088 (the remainder is 14, so 57 is not a divisor of 3377)
3377 / 58 = 58.224137931034 (the remainder is 13, so 58 is not a divisor of 3377)