What are the divisors of 1562?

1, 2, 11, 22, 71, 142, 781, 1562

There is a total of 8 positive divisors.
The sum of these divisors is 2592.
The arithmetic mean is 324.

4 even divisors

2, 22, 142, 1562

4 odd divisors

1, 11, 71, 781

How to compute the divisors of 1562?

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 1562 by each of the numbers from 1 to 1562 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)

1562 / 1 = 1562 (the remainder is 0, so 1 is a divisor of 1562)
1562 / 2 = 781 (the remainder is 0, so 2 is a divisor of 1562)
1562 / 3 = 520.66666666667 (the remainder is 2, so 3 is not a divisor of 1562)
...
1562 / 1561 = 1.0006406149904 (the remainder is 1, so 1561 is not a divisor of 1562)
1562 / 1562 = 1 (the remainder is 0, so 1562 is a divisor of 1562)

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 1562 (i.e. 39.522145690739). 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 $\frac{N}{d} = D$ )

1562 / 1 = 1562 (the remainder is 0, so 1 and 1562 are divisors of 1562)
1562 / 2 = 781 (the remainder is 0, so 2 and 781 are divisors of 1562)
1562 / 3 = 520.66666666667 (the remainder is 2, so 3 is not a divisor of 1562)
...
1562 / 38 = 41.105263157895 (the remainder is 4, so 38 is not a divisor of 1562)
1562 / 39 = 40.051282051282 (the remainder is 2, so 39 is not a divisor of 1562)