What are the divisors of 3570?

1, 2, 3, 5, 6, 7, 10, 14, 15, 17, 21, 30, 34, 35, 42, 51, 70, 85, 102, 105, 119, 170, 210, 238, 255, 357, 510, 595, 714, 1190, 1785, 3570

There is a total of 32 positive divisors.
The sum of these divisors is 10368.
The arithmetic mean is 324.

16 even divisors

2, 6, 10, 14, 30, 34, 42, 70, 102, 170, 210, 238, 510, 714, 1190, 3570

16 odd divisors

1, 3, 5, 7, 15, 17, 21, 35, 51, 85, 105, 119, 255, 357, 595, 1785

How to compute the divisors of 3570?

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 3570 by each of the numbers from 1 to 3570 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)

3570 / 1 = 3570 (the remainder is 0, so 1 is a divisor of 3570)
3570 / 2 = 1785 (the remainder is 0, so 2 is a divisor of 3570)
3570 / 3 = 1190 (the remainder is 0, so 3 is a divisor of 3570)
...
3570 / 3569 = 1.0002801905296 (the remainder is 1, so 3569 is not a divisor of 3570)
3570 / 3570 = 1 (the remainder is 0, so 3570 is a divisor of 3570)

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 3570 (i.e. 59.749476985159). 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 $\frac{N}{d} = D$ )

3570 / 1 = 3570 (the remainder is 0, so 1 and 3570 are divisors of 3570)
3570 / 2 = 1785 (the remainder is 0, so 2 and 1785 are divisors of 3570)
3570 / 3 = 1190 (the remainder is 0, so 3 and 1190 are divisors of 3570)
...
3570 / 58 = 61.551724137931 (the remainder is 32, so 58 is not a divisor of 3570)
3570 / 59 = 60.508474576271 (the remainder is 30, so 59 is not a divisor of 3570)