What are the divisors of 2141?

1, 2141

There is a total of 2 positive divisors.
The sum of these divisors is 2142.
The arithmetic mean is 1071.

2 odd divisors

1, 2141

How to compute the divisors of 2141?

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 2141 by each of the numbers from 1 to 2141 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)

2141 / 1 = 2141 (the remainder is 0, so 1 is a divisor of 2141)
2141 / 2 = 1070.5 (the remainder is 1, so 2 is not a divisor of 2141)
2141 / 3 = 713.66666666667 (the remainder is 2, so 3 is not a divisor of 2141)
...
2141 / 2140 = 1.0004672897196 (the remainder is 1, so 2140 is not a divisor of 2141)
2141 / 2141 = 1 (the remainder is 0, so 2141 is a divisor of 2141)

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 2141 (i.e. 46.270941205037). 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 $\frac{N}{d} = D$ )

2141 / 1 = 2141 (the remainder is 0, so 1 and 2141 are divisors of 2141)
2141 / 2 = 1070.5 (the remainder is 1, so 2 is not a divisor of 2141)
2141 / 3 = 713.66666666667 (the remainder is 2, so 3 is not a divisor of 2141)
...
2141 / 45 = 47.577777777778 (the remainder is 26, so 45 is not a divisor of 2141)
2141 / 46 = 46.54347826087 (the remainder is 25, so 46 is not a divisor of 2141)