What are the divisors of 1462?

1, 2, 17, 34, 43, 86, 731, 1462

There is a total of 8 positive divisors.
The sum of these divisors is 2376.
The arithmetic mean is 297.

4 even divisors

2, 34, 86, 1462

4 odd divisors

1, 17, 43, 731

How to compute the divisors of 1462?

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 1462 by each of the numbers from 1 to 1462 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)

1462 / 1 = 1462 (the remainder is 0, so 1 is a divisor of 1462)
1462 / 2 = 731 (the remainder is 0, so 2 is a divisor of 1462)
1462 / 3 = 487.33333333333 (the remainder is 1, so 3 is not a divisor of 1462)
...
1462 / 1461 = 1.0006844626968 (the remainder is 1, so 1461 is not a divisor of 1462)
1462 / 1462 = 1 (the remainder is 0, so 1462 is a divisor of 1462)

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 1462 (i.e. 38.23610858861). 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 $\frac{N}{d} = D$ )

1462 / 1 = 1462 (the remainder is 0, so 1 and 1462 are divisors of 1462)
1462 / 2 = 731 (the remainder is 0, so 2 and 731 are divisors of 1462)
1462 / 3 = 487.33333333333 (the remainder is 1, so 3 is not a divisor of 1462)
...
1462 / 37 = 39.513513513514 (the remainder is 19, so 37 is not a divisor of 1462)
1462 / 38 = 38.473684210526 (the remainder is 18, so 38 is not a divisor of 1462)