What are the divisors of 9637?

1, 23, 419, 9637

There is a total of 4 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 2520.

4 odd divisors

1, 23, 419, 9637

How to compute the divisors of 9637?

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 9637 by each of the numbers from 1 to 9637 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)

9637 / 1 = 9637 (the remainder is 0, so 1 is a divisor of 9637)
9637 / 2 = 4818.5 (the remainder is 1, so 2 is not a divisor of 9637)
9637 / 3 = 3212.3333333333 (the remainder is 1, so 3 is not a divisor of 9637)
...
9637 / 9636 = 1.000103777501 (the remainder is 1, so 9636 is not a divisor of 9637)
9637 / 9637 = 1 (the remainder is 0, so 9637 is a divisor of 9637)

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 9637 (i.e. 98.16822296446). 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 $\frac{N}{d} = D$ )

9637 / 1 = 9637 (the remainder is 0, so 1 and 9637 are divisors of 9637)
9637 / 2 = 4818.5 (the remainder is 1, so 2 is not a divisor of 9637)
9637 / 3 = 3212.3333333333 (the remainder is 1, so 3 is not a divisor of 9637)
...
9637 / 97 = 99.350515463918 (the remainder is 34, so 97 is not a divisor of 9637)
9637 / 98 = 98.336734693878 (the remainder is 33, so 98 is not a divisor of 9637)