What are the divisors of 562?

1, 2, 281, 562

There is a total of 4 positive divisors.
The sum of these divisors is 846.
The arithmetic mean is 211.5.

2 even divisors

2, 562

2 odd divisors

1, 281

How to compute the divisors of 562?

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 562 by each of the numbers from 1 to 562 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)

562 / 1 = 562 (the remainder is 0, so 1 is a divisor of 562)
562 / 2 = 281 (the remainder is 0, so 2 is a divisor of 562)
562 / 3 = 187.33333333333 (the remainder is 1, so 3 is not a divisor of 562)
...
562 / 561 = 1.0017825311943 (the remainder is 1, so 561 is not a divisor of 562)
562 / 562 = 1 (the remainder is 0, so 562 is a divisor of 562)

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 562 (i.e. 23.706539182259). 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 $\frac{N}{d} = D$ )

562 / 1 = 562 (the remainder is 0, so 1 and 562 are divisors of 562)
562 / 2 = 281 (the remainder is 0, so 2 and 281 are divisors of 562)
562 / 3 = 187.33333333333 (the remainder is 1, so 3 is not a divisor of 562)
...
562 / 22 = 25.545454545455 (the remainder is 12, so 22 is not a divisor of 562)
562 / 23 = 24.434782608696 (the remainder is 10, so 23 is not a divisor of 562)