What are the divisors of 3572?

1, 2, 4, 19, 38, 47, 76, 94, 188, 893, 1786, 3572

There is a total of 12 positive divisors.
The sum of these divisors is 6720.
The arithmetic mean is 560.

8 even divisors

2, 4, 38, 76, 94, 188, 1786, 3572

4 odd divisors

1, 19, 47, 893

How to compute the divisors of 3572?

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 3572 by each of the numbers from 1 to 3572 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)

3572 / 1 = 3572 (the remainder is 0, so 1 is a divisor of 3572)
3572 / 2 = 1786 (the remainder is 0, so 2 is a divisor of 3572)
3572 / 3 = 1190.6666666667 (the remainder is 2, so 3 is not a divisor of 3572)
...
3572 / 3571 = 1.000280033604 (the remainder is 1, so 3571 is not a divisor of 3572)
3572 / 3572 = 1 (the remainder is 0, so 3572 is a divisor of 3572)

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 3572 (i.e. 59.766211189936). 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 $\frac{N}{d} = D$ )

3572 / 1 = 3572 (the remainder is 0, so 1 and 3572 are divisors of 3572)
3572 / 2 = 1786 (the remainder is 0, so 2 and 1786 are divisors of 3572)
3572 / 3 = 1190.6666666667 (the remainder is 2, so 3 is not a divisor of 3572)
...
3572 / 58 = 61.586206896552 (the remainder is 34, so 58 is not a divisor of 3572)
3572 / 59 = 60.542372881356 (the remainder is 32, so 59 is not a divisor of 3572)