What are the divisors of 2527?

1, 7, 19, 133, 361, 2527

There is a total of 6 positive divisors.
The sum of these divisors is 3048.
The arithmetic mean is 508.

6 odd divisors

1, 7, 19, 133, 361, 2527

How to compute the divisors of 2527?

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 2527 by each of the numbers from 1 to 2527 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)

2527 / 1 = 2527 (the remainder is 0, so 1 is a divisor of 2527)
2527 / 2 = 1263.5 (the remainder is 1, so 2 is not a divisor of 2527)
2527 / 3 = 842.33333333333 (the remainder is 1, so 3 is not a divisor of 2527)
...
2527 / 2526 = 1.0003958828187 (the remainder is 1, so 2526 is not a divisor of 2527)
2527 / 2527 = 1 (the remainder is 0, so 2527 is a divisor of 2527)

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 2527 (i.e. 50.269274910227). 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 $\frac{N}{d} = D$ )

2527 / 1 = 2527 (the remainder is 0, so 1 and 2527 are divisors of 2527)
2527 / 2 = 1263.5 (the remainder is 1, so 2 is not a divisor of 2527)
2527 / 3 = 842.33333333333 (the remainder is 1, so 3 is not a divisor of 2527)
...
2527 / 49 = 51.571428571429 (the remainder is 28, so 49 is not a divisor of 2527)
2527 / 50 = 50.54 (the remainder is 27, so 50 is not a divisor of 2527)