What are the divisors of 3062?

1, 2, 1531, 3062

There is a total of 4 positive divisors.
The sum of these divisors is 4596.
The arithmetic mean is 1149.

2 even divisors

2, 3062

2 odd divisors

1, 1531

How to compute the divisors of 3062?

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 3062 by each of the numbers from 1 to 3062 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)

3062 / 1 = 3062 (the remainder is 0, so 1 is a divisor of 3062)
3062 / 2 = 1531 (the remainder is 0, so 2 is a divisor of 3062)
3062 / 3 = 1020.6666666667 (the remainder is 2, so 3 is not a divisor of 3062)
...
3062 / 3061 = 1.000326690624 (the remainder is 1, so 3061 is not a divisor of 3062)
3062 / 3062 = 1 (the remainder is 0, so 3062 is a divisor of 3062)

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 3062 (i.e. 55.335341329028). 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 $\frac{N}{d} = D$ )

3062 / 1 = 3062 (the remainder is 0, so 1 and 3062 are divisors of 3062)
3062 / 2 = 1531 (the remainder is 0, so 2 and 1531 are divisors of 3062)
3062 / 3 = 1020.6666666667 (the remainder is 2, so 3 is not a divisor of 3062)
...
3062 / 54 = 56.703703703704 (the remainder is 38, so 54 is not a divisor of 3062)
3062 / 55 = 55.672727272727 (the remainder is 37, so 55 is not a divisor of 3062)