What are the divisors of 2102?

1, 2, 1051, 2102

There is a total of 4 positive divisors.
The sum of these divisors is 3156.
The arithmetic mean is 789.

2 even divisors

2, 2102

2 odd divisors

1, 1051

How to compute the divisors of 2102?

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 2102 by each of the numbers from 1 to 2102 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)

2102 / 1 = 2102 (the remainder is 0, so 1 is a divisor of 2102)
2102 / 2 = 1051 (the remainder is 0, so 2 is a divisor of 2102)
2102 / 3 = 700.66666666667 (the remainder is 2, so 3 is not a divisor of 2102)
...
2102 / 2101 = 1.0004759638267 (the remainder is 1, so 2101 is not a divisor of 2102)
2102 / 2102 = 1 (the remainder is 0, so 2102 is a divisor of 2102)

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 2102 (i.e. 45.847573545391). 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 $\frac{N}{d} = D$ )

2102 / 1 = 2102 (the remainder is 0, so 1 and 2102 are divisors of 2102)
2102 / 2 = 1051 (the remainder is 0, so 2 and 1051 are divisors of 2102)
2102 / 3 = 700.66666666667 (the remainder is 2, so 3 is not a divisor of 2102)
...
2102 / 44 = 47.772727272727 (the remainder is 34, so 44 is not a divisor of 2102)
2102 / 45 = 46.711111111111 (the remainder is 32, so 45 is not a divisor of 2102)