What are the divisors of 1198?

1, 2, 599, 1198

There is a total of 4 positive divisors.
The sum of these divisors is 1800.
The arithmetic mean is 450.

2 even divisors

2, 1198

2 odd divisors

1, 599

How to compute the divisors of 1198?

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 1198 by each of the numbers from 1 to 1198 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)

1198 / 1 = 1198 (the remainder is 0, so 1 is a divisor of 1198)
1198 / 2 = 599 (the remainder is 0, so 2 is a divisor of 1198)
1198 / 3 = 399.33333333333 (the remainder is 1, so 3 is not a divisor of 1198)
...
1198 / 1197 = 1.0008354218881 (the remainder is 1, so 1197 is not a divisor of 1198)
1198 / 1198 = 1 (the remainder is 0, so 1198 is a divisor of 1198)

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 1198 (i.e. 34.612136599754). 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 $\frac{N}{d} = D$ )

1198 / 1 = 1198 (the remainder is 0, so 1 and 1198 are divisors of 1198)
1198 / 2 = 599 (the remainder is 0, so 2 and 599 are divisors of 1198)
1198 / 3 = 399.33333333333 (the remainder is 1, so 3 is not a divisor of 1198)
...
1198 / 33 = 36.30303030303 (the remainder is 10, so 33 is not a divisor of 1198)
1198 / 34 = 35.235294117647 (the remainder is 8, so 34 is not a divisor of 1198)