What are the divisors of 2890?

1, 2, 5, 10, 17, 34, 85, 170, 289, 578, 1445, 2890

There is a total of 12 positive divisors.
The sum of these divisors is 5526.
The arithmetic mean is 460.5.

6 even divisors

2, 10, 34, 170, 578, 2890

6 odd divisors

1, 5, 17, 85, 289, 1445

How to compute the divisors of 2890?

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 2890 by each of the numbers from 1 to 2890 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)

2890 / 1 = 2890 (the remainder is 0, so 1 is a divisor of 2890)
2890 / 2 = 1445 (the remainder is 0, so 2 is a divisor of 2890)
2890 / 3 = 963.33333333333 (the remainder is 1, so 3 is not a divisor of 2890)
...
2890 / 2889 = 1.0003461405331 (the remainder is 1, so 2889 is not a divisor of 2890)
2890 / 2890 = 1 (the remainder is 0, so 2890 is a divisor of 2890)

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 2890 (i.e. 53.758720222862). 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 $\frac{N}{d} = D$ )

2890 / 1 = 2890 (the remainder is 0, so 1 and 2890 are divisors of 2890)
2890 / 2 = 1445 (the remainder is 0, so 2 and 1445 are divisors of 2890)
2890 / 3 = 963.33333333333 (the remainder is 1, so 3 is not a divisor of 2890)
...
2890 / 52 = 55.576923076923 (the remainder is 30, so 52 is not a divisor of 2890)
2890 / 53 = 54.528301886792 (the remainder is 28, so 53 is not a divisor of 2890)