What are the divisors of 3098?

1, 2, 1549, 3098

There is a total of 4 positive divisors.
The sum of these divisors is 4650.
The arithmetic mean is 1162.5.

2 even divisors

2, 3098

2 odd divisors

1, 1549

How to compute the divisors of 3098?

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 3098 by each of the numbers from 1 to 3098 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)

3098 / 1 = 3098 (the remainder is 0, so 1 is a divisor of 3098)
3098 / 2 = 1549 (the remainder is 0, so 2 is a divisor of 3098)
3098 / 3 = 1032.6666666667 (the remainder is 2, so 3 is not a divisor of 3098)
...
3098 / 3097 = 1.0003228931224 (the remainder is 1, so 3097 is not a divisor of 3098)
3098 / 3098 = 1 (the remainder is 0, so 3098 is a divisor of 3098)

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 3098 (i.e. 55.659680200303). 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 $\frac{N}{d} = D$ )

3098 / 1 = 3098 (the remainder is 0, so 1 and 3098 are divisors of 3098)
3098 / 2 = 1549 (the remainder is 0, so 2 and 1549 are divisors of 3098)
3098 / 3 = 1032.6666666667 (the remainder is 2, so 3 is not a divisor of 3098)
...
3098 / 54 = 57.37037037037 (the remainder is 20, so 54 is not a divisor of 3098)
3098 / 55 = 56.327272727273 (the remainder is 18, so 55 is not a divisor of 3098)