What are the divisors of 9602?

1, 2, 4801, 9602

There is a total of 4 positive divisors.
The sum of these divisors is 14406.
The arithmetic mean is 3601.5.

2 even divisors

2, 9602

2 odd divisors

1, 4801

How to compute the divisors of 9602?

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 9602 by each of the numbers from 1 to 9602 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)

9602 / 1 = 9602 (the remainder is 0, so 1 is a divisor of 9602)
9602 / 2 = 4801 (the remainder is 0, so 2 is a divisor of 9602)
9602 / 3 = 3200.6666666667 (the remainder is 2, so 3 is not a divisor of 9602)
...
9602 / 9601 = 1.0001041558171 (the remainder is 1, so 9601 is not a divisor of 9602)
9602 / 9602 = 1 (the remainder is 0, so 9602 is a divisor of 9602)

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 9602 (i.e. 97.989795387071). 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 $\frac{N}{d} = D$ )

9602 / 1 = 9602 (the remainder is 0, so 1 and 9602 are divisors of 9602)
9602 / 2 = 4801 (the remainder is 0, so 2 and 4801 are divisors of 9602)
9602 / 3 = 3200.6666666667 (the remainder is 2, so 3 is not a divisor of 9602)
...
9602 / 96 = 100.02083333333 (the remainder is 2, so 96 is not a divisor of 9602)
9602 / 97 = 98.989690721649 (the remainder is 96, so 97 is not a divisor of 9602)