What are the divisors of 9598?

1, 2, 4799, 9598

There is a total of 4 positive divisors.
The sum of these divisors is 14400.
The arithmetic mean is 3600.

2 even divisors

2, 9598

2 odd divisors

1, 4799

How to compute the divisors of 9598?

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 9598 by each of the numbers from 1 to 9598 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)

9598 / 1 = 9598 (the remainder is 0, so 1 is a divisor of 9598)
9598 / 2 = 4799 (the remainder is 0, so 2 is a divisor of 9598)
9598 / 3 = 3199.3333333333 (the remainder is 1, so 3 is not a divisor of 9598)
...
9598 / 9597 = 1.0001041992289 (the remainder is 1, so 9597 is not a divisor of 9598)
9598 / 9598 = 1 (the remainder is 0, so 9598 is a divisor of 9598)

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 9598 (i.e. 97.969382972437). 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 $\frac{N}{d} = D$ )

9598 / 1 = 9598 (the remainder is 0, so 1 and 9598 are divisors of 9598)
9598 / 2 = 4799 (the remainder is 0, so 2 and 4799 are divisors of 9598)
9598 / 3 = 3199.3333333333 (the remainder is 1, so 3 is not a divisor of 9598)
...
9598 / 96 = 99.979166666667 (the remainder is 94, so 96 is not a divisor of 9598)
9598 / 97 = 98.948453608247 (the remainder is 92, so 97 is not a divisor of 9598)