What are the divisors of 2989?

1, 7, 49, 61, 427, 2989

There is a total of 6 positive divisors.
The sum of these divisors is 3534.
The arithmetic mean is 589.

6 odd divisors

1, 7, 49, 61, 427, 2989

How to compute the divisors of 2989?

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 2989 by each of the numbers from 1 to 2989 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)

2989 / 1 = 2989 (the remainder is 0, so 1 is a divisor of 2989)
2989 / 2 = 1494.5 (the remainder is 1, so 2 is not a divisor of 2989)
2989 / 3 = 996.33333333333 (the remainder is 1, so 3 is not a divisor of 2989)
...
2989 / 2988 = 1.0003346720214 (the remainder is 1, so 2988 is not a divisor of 2989)
2989 / 2989 = 1 (the remainder is 0, so 2989 is a divisor of 2989)

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 2989 (i.e. 54.671747731347). 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 $\frac{N}{d} = D$ )

2989 / 1 = 2989 (the remainder is 0, so 1 and 2989 are divisors of 2989)
2989 / 2 = 1494.5 (the remainder is 1, so 2 is not a divisor of 2989)
2989 / 3 = 996.33333333333 (the remainder is 1, so 3 is not a divisor of 2989)
...
2989 / 53 = 56.396226415094 (the remainder is 21, so 53 is not a divisor of 2989)
2989 / 54 = 55.351851851852 (the remainder is 19, so 54 is not a divisor of 2989)