What are the divisors of 5249?

1, 29, 181, 5249

There is a total of 4 positive divisors.
The sum of these divisors is 5460.
The arithmetic mean is 1365.

4 odd divisors

1, 29, 181, 5249

How to compute the divisors of 5249?

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 5249 by each of the numbers from 1 to 5249 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)

5249 / 1 = 5249 (the remainder is 0, so 1 is a divisor of 5249)
5249 / 2 = 2624.5 (the remainder is 1, so 2 is not a divisor of 5249)
5249 / 3 = 1749.6666666667 (the remainder is 2, so 3 is not a divisor of 5249)
...
5249 / 5248 = 1.0001905487805 (the remainder is 1, so 5248 is not a divisor of 5249)
5249 / 5249 = 1 (the remainder is 0, so 5249 is a divisor of 5249)

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 5249 (i.e. 72.44998274672). 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 $\frac{N}{d} = D$ )

5249 / 1 = 5249 (the remainder is 0, so 1 and 5249 are divisors of 5249)
5249 / 2 = 2624.5 (the remainder is 1, so 2 is not a divisor of 5249)
5249 / 3 = 1749.6666666667 (the remainder is 2, so 3 is not a divisor of 5249)
...
5249 / 71 = 73.929577464789 (the remainder is 66, so 71 is not a divisor of 5249)
5249 / 72 = 72.902777777778 (the remainder is 65, so 72 is not a divisor of 5249)