What are the divisors of 5270?

1, 2, 5, 10, 17, 31, 34, 62, 85, 155, 170, 310, 527, 1054, 2635, 5270

There is a total of 16 positive divisors.
The sum of these divisors is 10368.
The arithmetic mean is 648.

8 even divisors

2, 10, 34, 62, 170, 310, 1054, 5270

8 odd divisors

1, 5, 17, 31, 85, 155, 527, 2635

How to compute the divisors of 5270?

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 5270 by each of the numbers from 1 to 5270 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)

5270 / 1 = 5270 (the remainder is 0, so 1 is a divisor of 5270)
5270 / 2 = 2635 (the remainder is 0, so 2 is a divisor of 5270)
5270 / 3 = 1756.6666666667 (the remainder is 2, so 3 is not a divisor of 5270)
...
5270 / 5269 = 1.0001897893338 (the remainder is 1, so 5269 is not a divisor of 5270)
5270 / 5270 = 1 (the remainder is 0, so 5270 is a divisor of 5270)

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 5270 (i.e. 72.594765651526). 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 $\frac{N}{d} = D$ )

5270 / 1 = 5270 (the remainder is 0, so 1 and 5270 are divisors of 5270)
5270 / 2 = 2635 (the remainder is 0, so 2 and 2635 are divisors of 5270)
5270 / 3 = 1756.6666666667 (the remainder is 2, so 3 is not a divisor of 5270)
...
5270 / 71 = 74.225352112676 (the remainder is 16, so 71 is not a divisor of 5270)
5270 / 72 = 73.194444444444 (the remainder is 14, so 72 is not a divisor of 5270)