What are the divisors of 4462?

1, 2, 23, 46, 97, 194, 2231, 4462

There is a total of 8 positive divisors.
The sum of these divisors is 7056.
The arithmetic mean is 882.

4 even divisors

2, 46, 194, 4462

4 odd divisors

1, 23, 97, 2231

How to compute the divisors of 4462?

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 4462 by each of the numbers from 1 to 4462 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)

4462 / 1 = 4462 (the remainder is 0, so 1 is a divisor of 4462)
4462 / 2 = 2231 (the remainder is 0, so 2 is a divisor of 4462)
4462 / 3 = 1487.3333333333 (the remainder is 1, so 3 is not a divisor of 4462)
...
4462 / 4461 = 1.0002241649854 (the remainder is 1, so 4461 is not a divisor of 4462)
4462 / 4462 = 1 (the remainder is 0, so 4462 is a divisor of 4462)

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 4462 (i.e. 66.798203568659). 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 $\frac{N}{d} = D$ )

4462 / 1 = 4462 (the remainder is 0, so 1 and 4462 are divisors of 4462)
4462 / 2 = 2231 (the remainder is 0, so 2 and 2231 are divisors of 4462)
4462 / 3 = 1487.3333333333 (the remainder is 1, so 3 is not a divisor of 4462)
...
4462 / 65 = 68.646153846154 (the remainder is 42, so 65 is not a divisor of 4462)
4462 / 66 = 67.606060606061 (the remainder is 40, so 66 is not a divisor of 4462)