What are the divisors of 4495?

1, 5, 29, 31, 145, 155, 899, 4495

There is a total of 8 positive divisors.
The sum of these divisors is 5760.
The arithmetic mean is 720.

8 odd divisors

1, 5, 29, 31, 145, 155, 899, 4495

How to compute the divisors of 4495?

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 4495 by each of the numbers from 1 to 4495 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)

4495 / 1 = 4495 (the remainder is 0, so 1 is a divisor of 4495)
4495 / 2 = 2247.5 (the remainder is 1, so 2 is not a divisor of 4495)
4495 / 3 = 1498.3333333333 (the remainder is 1, so 3 is not a divisor of 4495)
...
4495 / 4494 = 1.0002225189141 (the remainder is 1, so 4494 is not a divisor of 4495)
4495 / 4495 = 1 (the remainder is 0, so 4495 is a divisor of 4495)

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 4495 (i.e. 67.044761167447). 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 $\frac{N}{d} = D$ )

4495 / 1 = 4495 (the remainder is 0, so 1 and 4495 are divisors of 4495)
4495 / 2 = 2247.5 (the remainder is 1, so 2 is not a divisor of 4495)
4495 / 3 = 1498.3333333333 (the remainder is 1, so 3 is not a divisor of 4495)
...
4495 / 66 = 68.106060606061 (the remainder is 7, so 66 is not a divisor of 4495)
4495 / 67 = 67.089552238806 (the remainder is 6, so 67 is not a divisor of 4495)