What are the divisors of 3477?

1, 3, 19, 57, 61, 183, 1159, 3477

There is a total of 8 positive divisors.
The sum of these divisors is 4960.
The arithmetic mean is 620.

8 odd divisors

1, 3, 19, 57, 61, 183, 1159, 3477

How to compute the divisors of 3477?

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 3477 by each of the numbers from 1 to 3477 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)

3477 / 1 = 3477 (the remainder is 0, so 1 is a divisor of 3477)
3477 / 2 = 1738.5 (the remainder is 1, so 2 is not a divisor of 3477)
3477 / 3 = 1159 (the remainder is 0, so 3 is a divisor of 3477)
...
3477 / 3476 = 1.0002876869965 (the remainder is 1, so 3476 is not a divisor of 3477)
3477 / 3477 = 1 (the remainder is 0, so 3477 is a divisor of 3477)

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 3477 (i.e. 58.966091951222). 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 $\frac{N}{d} = D$ )

3477 / 1 = 3477 (the remainder is 0, so 1 and 3477 are divisors of 3477)
3477 / 2 = 1738.5 (the remainder is 1, so 2 is not a divisor of 3477)
3477 / 3 = 1159 (the remainder is 0, so 3 and 1159 are divisors of 3477)
...
3477 / 57 = 61 (the remainder is 0, so 57 and 61 are divisors of 3477)
3477 / 58 = 59.948275862069 (the remainder is 55, so 58 is not a divisor of 3477)