What are the divisors of 2888?

1, 2, 4, 8, 19, 38, 76, 152, 361, 722, 1444, 2888

There is a total of 12 positive divisors.
The sum of these divisors is 5715.
The arithmetic mean is 476.25.

9 even divisors

2, 4, 8, 38, 76, 152, 722, 1444, 2888

3 odd divisors

1, 19, 361

How to compute the divisors of 2888?

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 2888 by each of the numbers from 1 to 2888 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)

2888 / 1 = 2888 (the remainder is 0, so 1 is a divisor of 2888)
2888 / 2 = 1444 (the remainder is 0, so 2 is a divisor of 2888)
2888 / 3 = 962.66666666667 (the remainder is 2, so 3 is not a divisor of 2888)
...
2888 / 2887 = 1.0003463803256 (the remainder is 1, so 2887 is not a divisor of 2888)
2888 / 2888 = 1 (the remainder is 0, so 2888 is a divisor of 2888)

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 2888 (i.e. 53.740115370178). 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 $\frac{N}{d} = D$ )

2888 / 1 = 2888 (the remainder is 0, so 1 and 2888 are divisors of 2888)
2888 / 2 = 1444 (the remainder is 0, so 2 and 1444 are divisors of 2888)
2888 / 3 = 962.66666666667 (the remainder is 2, so 3 is not a divisor of 2888)
...
2888 / 52 = 55.538461538462 (the remainder is 28, so 52 is not a divisor of 2888)
2888 / 53 = 54.490566037736 (the remainder is 26, so 53 is not a divisor of 2888)