What are the divisors of 4133?

1, 4133

There is a total of 2 positive divisors.
The sum of these divisors is 4134.
The arithmetic mean is 2067.

2 odd divisors

1, 4133

How to compute the divisors of 4133?

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 4133 by each of the numbers from 1 to 4133 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)

4133 / 1 = 4133 (the remainder is 0, so 1 is a divisor of 4133)
4133 / 2 = 2066.5 (the remainder is 1, so 2 is not a divisor of 4133)
4133 / 3 = 1377.6666666667 (the remainder is 2, so 3 is not a divisor of 4133)
...
4133 / 4132 = 1.0002420135528 (the remainder is 1, so 4132 is not a divisor of 4133)
4133 / 4133 = 1 (the remainder is 0, so 4133 is a divisor of 4133)

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 4133 (i.e. 64.288412641782). 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 $\frac{N}{d} = D$ )

4133 / 1 = 4133 (the remainder is 0, so 1 and 4133 are divisors of 4133)
4133 / 2 = 2066.5 (the remainder is 1, so 2 is not a divisor of 4133)
4133 / 3 = 1377.6666666667 (the remainder is 2, so 3 is not a divisor of 4133)
...
4133 / 63 = 65.603174603175 (the remainder is 38, so 63 is not a divisor of 4133)
4133 / 64 = 64.578125 (the remainder is 37, so 64 is not a divisor of 4133)