What are the divisors of 2062?

1, 2, 1031, 2062

There is a total of 4 positive divisors.
The sum of these divisors is 3096.
The arithmetic mean is 774.

2 even divisors

2, 2062

2 odd divisors

1, 1031

How to compute the divisors of 2062?

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 2062 by each of the numbers from 1 to 2062 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)

2062 / 1 = 2062 (the remainder is 0, so 1 is a divisor of 2062)
2062 / 2 = 1031 (the remainder is 0, so 2 is a divisor of 2062)
2062 / 3 = 687.33333333333 (the remainder is 1, so 3 is not a divisor of 2062)
...
2062 / 2061 = 1.0004852013586 (the remainder is 1, so 2061 is not a divisor of 2062)
2062 / 2062 = 1 (the remainder is 0, so 2062 is a divisor of 2062)

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 2062 (i.e. 45.409250158971). 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 $\frac{N}{d} = D$ )

2062 / 1 = 2062 (the remainder is 0, so 1 and 2062 are divisors of 2062)
2062 / 2 = 1031 (the remainder is 0, so 2 and 1031 are divisors of 2062)
2062 / 3 = 687.33333333333 (the remainder is 1, so 3 is not a divisor of 2062)
...
2062 / 44 = 46.863636363636 (the remainder is 38, so 44 is not a divisor of 2062)
2062 / 45 = 45.822222222222 (the remainder is 37, so 45 is not a divisor of 2062)