What are the divisors of 4053?

1, 3, 7, 21, 193, 579, 1351, 4053

There is a total of 8 positive divisors.
The sum of these divisors is 6208.
The arithmetic mean is 776.

8 odd divisors

1, 3, 7, 21, 193, 579, 1351, 4053

How to compute the divisors of 4053?

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 4053 by each of the numbers from 1 to 4053 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)

4053 / 1 = 4053 (the remainder is 0, so 1 is a divisor of 4053)
4053 / 2 = 2026.5 (the remainder is 1, so 2 is not a divisor of 4053)
4053 / 3 = 1351 (the remainder is 0, so 3 is a divisor of 4053)
...
4053 / 4052 = 1.0002467917078 (the remainder is 1, so 4052 is not a divisor of 4053)
4053 / 4053 = 1 (the remainder is 0, so 4053 is a divisor of 4053)

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 4053 (i.e. 63.663176169588). 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 $\frac{N}{d} = D$ )

4053 / 1 = 4053 (the remainder is 0, so 1 and 4053 are divisors of 4053)
4053 / 2 = 2026.5 (the remainder is 1, so 2 is not a divisor of 4053)
4053 / 3 = 1351 (the remainder is 0, so 3 and 1351 are divisors of 4053)
...
4053 / 62 = 65.370967741935 (the remainder is 23, so 62 is not a divisor of 4053)
4053 / 63 = 64.333333333333 (the remainder is 21, so 63 is not a divisor of 4053)