What are the divisors of 3562?

1, 2, 13, 26, 137, 274, 1781, 3562

There is a total of 8 positive divisors.
The sum of these divisors is 5796.
The arithmetic mean is 724.5.

4 even divisors

2, 26, 274, 3562

4 odd divisors

1, 13, 137, 1781

How to compute the divisors of 3562?

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 3562 by each of the numbers from 1 to 3562 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)

3562 / 1 = 3562 (the remainder is 0, so 1 is a divisor of 3562)
3562 / 2 = 1781 (the remainder is 0, so 2 is a divisor of 3562)
3562 / 3 = 1187.3333333333 (the remainder is 1, so 3 is not a divisor of 3562)
...
3562 / 3561 = 1.0002808199944 (the remainder is 1, so 3561 is not a divisor of 3562)
3562 / 3562 = 1 (the remainder is 0, so 3562 is a divisor of 3562)

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 3562 (i.e. 59.682493245507). 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 $\frac{N}{d} = D$ )

3562 / 1 = 3562 (the remainder is 0, so 1 and 3562 are divisors of 3562)
3562 / 2 = 1781 (the remainder is 0, so 2 and 1781 are divisors of 3562)
3562 / 3 = 1187.3333333333 (the remainder is 1, so 3 is not a divisor of 3562)
...
3562 / 58 = 61.413793103448 (the remainder is 24, so 58 is not a divisor of 3562)
3562 / 59 = 60.372881355932 (the remainder is 22, so 59 is not a divisor of 3562)