What are the divisors of 4273?

1, 4273

There is a total of 2 positive divisors.
The sum of these divisors is 4274.
The arithmetic mean is 2137.

2 odd divisors

1, 4273

How to compute the divisors of 4273?

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 4273 by each of the numbers from 1 to 4273 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)

4273 / 1 = 4273 (the remainder is 0, so 1 is a divisor of 4273)
4273 / 2 = 2136.5 (the remainder is 1, so 2 is not a divisor of 4273)
4273 / 3 = 1424.3333333333 (the remainder is 1, so 3 is not a divisor of 4273)
...
4273 / 4272 = 1.000234082397 (the remainder is 1, so 4272 is not a divisor of 4273)
4273 / 4273 = 1 (the remainder is 0, so 4273 is a divisor of 4273)

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 4273 (i.e. 65.368187981617). 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 $\frac{N}{d} = D$ )

4273 / 1 = 4273 (the remainder is 0, so 1 and 4273 are divisors of 4273)
4273 / 2 = 2136.5 (the remainder is 1, so 2 is not a divisor of 4273)
4273 / 3 = 1424.3333333333 (the remainder is 1, so 3 is not a divisor of 4273)
...
4273 / 64 = 66.765625 (the remainder is 49, so 64 is not a divisor of 4273)
4273 / 65 = 65.738461538462 (the remainder is 48, so 65 is not a divisor of 4273)