What are the divisors of 4263?

1, 3, 7, 21, 29, 49, 87, 147, 203, 609, 1421, 4263

There is a total of 12 positive divisors.
The sum of these divisors is 6840.
The arithmetic mean is 570.

12 odd divisors

1, 3, 7, 21, 29, 49, 87, 147, 203, 609, 1421, 4263

How to compute the divisors of 4263?

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 4263 by each of the numbers from 1 to 4263 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)

4263 / 1 = 4263 (the remainder is 0, so 1 is a divisor of 4263)
4263 / 2 = 2131.5 (the remainder is 1, so 2 is not a divisor of 4263)
4263 / 3 = 1421 (the remainder is 0, so 3 is a divisor of 4263)
...
4263 / 4262 = 1.0002346316283 (the remainder is 1, so 4262 is not a divisor of 4263)
4263 / 4263 = 1 (the remainder is 0, so 4263 is a divisor of 4263)

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 4263 (i.e. 65.291653371622). 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 $\frac{N}{d} = D$ )

4263 / 1 = 4263 (the remainder is 0, so 1 and 4263 are divisors of 4263)
4263 / 2 = 2131.5 (the remainder is 1, so 2 is not a divisor of 4263)
4263 / 3 = 1421 (the remainder is 0, so 3 and 1421 are divisors of 4263)
...
4263 / 64 = 66.609375 (the remainder is 39, so 64 is not a divisor of 4263)
4263 / 65 = 65.584615384615 (the remainder is 38, so 65 is not a divisor of 4263)