What are the divisors of 298?

1, 2, 149, 298

There is a total of 4 positive divisors.
The sum of these divisors is 450.
The arithmetic mean is 112.5.

2 even divisors

2, 298

2 odd divisors

1, 149

How to compute the divisors of 298?

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 298 by each of the numbers from 1 to 298 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)

298 / 1 = 298 (the remainder is 0, so 1 is a divisor of 298)
298 / 2 = 149 (the remainder is 0, so 2 is a divisor of 298)
298 / 3 = 99.333333333333 (the remainder is 1, so 3 is not a divisor of 298)
...
298 / 297 = 1.003367003367 (the remainder is 1, so 297 is not a divisor of 298)
298 / 298 = 1 (the remainder is 0, so 298 is a divisor of 298)

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 298 (i.e. 17.262676501632). 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 $\frac{N}{d} = D$ )

298 / 1 = 298 (the remainder is 0, so 1 and 298 are divisors of 298)
298 / 2 = 149 (the remainder is 0, so 2 and 149 are divisors of 298)
298 / 3 = 99.333333333333 (the remainder is 1, so 3 is not a divisor of 298)
...
298 / 16 = 18.625 (the remainder is 10, so 16 is not a divisor of 298)
298 / 17 = 17.529411764706 (the remainder is 9, so 17 is not a divisor of 298)