What are the divisors of 3480?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 29, 30, 40, 58, 60, 87, 116, 120, 145, 174, 232, 290, 348, 435, 580, 696, 870, 1160, 1740, 3480

There is a total of 32 positive divisors.
The sum of these divisors is 10800.
The arithmetic mean is 337.5.

24 even divisors

2, 4, 6, 8, 10, 12, 20, 24, 30, 40, 58, 60, 116, 120, 174, 232, 290, 348, 580, 696, 870, 1160, 1740, 3480

8 odd divisors

1, 3, 5, 15, 29, 87, 145, 435

How to compute the divisors of 3480?

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 3480 by each of the numbers from 1 to 3480 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)

3480 / 1 = 3480 (the remainder is 0, so 1 is a divisor of 3480)
3480 / 2 = 1740 (the remainder is 0, so 2 is a divisor of 3480)
3480 / 3 = 1160 (the remainder is 0, so 3 is a divisor of 3480)
...
3480 / 3479 = 1.0002874389192 (the remainder is 1, so 3479 is not a divisor of 3480)
3480 / 3480 = 1 (the remainder is 0, so 3480 is a divisor of 3480)

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 3480 (i.e. 58.991524815011). 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 $\frac{N}{d} = D$ )

3480 / 1 = 3480 (the remainder is 0, so 1 and 3480 are divisors of 3480)
3480 / 2 = 1740 (the remainder is 0, so 2 and 1740 are divisors of 3480)
3480 / 3 = 1160 (the remainder is 0, so 3 and 1160 are divisors of 3480)
...
3480 / 57 = 61.052631578947 (the remainder is 3, so 57 is not a divisor of 3480)
3480 / 58 = 60 (the remainder is 0, so 58 and 60 are divisors of 3480)