What are the divisors of 4262?

1, 2, 2131, 4262

There is a total of 4 positive divisors.
The sum of these divisors is 6396.
The arithmetic mean is 1599.

2 even divisors

2, 4262

2 odd divisors

1, 2131

How to compute the divisors of 4262?

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 4262 by each of the numbers from 1 to 4262 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)

4262 / 1 = 4262 (the remainder is 0, so 1 is a divisor of 4262)
4262 / 2 = 2131 (the remainder is 0, so 2 is a divisor of 4262)
4262 / 3 = 1420.6666666667 (the remainder is 2, so 3 is not a divisor of 4262)
...
4262 / 4261 = 1.0002346866933 (the remainder is 1, so 4261 is not a divisor of 4262)
4262 / 4262 = 1 (the remainder is 0, so 4262 is a divisor of 4262)

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 4262 (i.e. 65.283994975798). 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 $\frac{N}{d} = D$ )

4262 / 1 = 4262 (the remainder is 0, so 1 and 4262 are divisors of 4262)
4262 / 2 = 2131 (the remainder is 0, so 2 and 2131 are divisors of 4262)
4262 / 3 = 1420.6666666667 (the remainder is 2, so 3 is not a divisor of 4262)
...
4262 / 64 = 66.59375 (the remainder is 38, so 64 is not a divisor of 4262)
4262 / 65 = 65.569230769231 (the remainder is 37, so 65 is not a divisor of 4262)