What are the divisors of 2354?

1, 2, 11, 22, 107, 214, 1177, 2354

There is a total of 8 positive divisors.
The sum of these divisors is 3888.
The arithmetic mean is 486.

4 even divisors

2, 22, 214, 2354

4 odd divisors

1, 11, 107, 1177

How to compute the divisors of 2354?

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 2354 by each of the numbers from 1 to 2354 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)

2354 / 1 = 2354 (the remainder is 0, so 1 is a divisor of 2354)
2354 / 2 = 1177 (the remainder is 0, so 2 is a divisor of 2354)
2354 / 3 = 784.66666666667 (the remainder is 2, so 3 is not a divisor of 2354)
...
2354 / 2353 = 1.0004249893753 (the remainder is 1, so 2353 is not a divisor of 2354)
2354 / 2354 = 1 (the remainder is 0, so 2354 is a divisor of 2354)

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 2354 (i.e. 48.518037882833). 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 $\frac{N}{d} = D$ )

2354 / 1 = 2354 (the remainder is 0, so 1 and 2354 are divisors of 2354)
2354 / 2 = 1177 (the remainder is 0, so 2 and 1177 are divisors of 2354)
2354 / 3 = 784.66666666667 (the remainder is 2, so 3 is not a divisor of 2354)
...
2354 / 47 = 50.085106382979 (the remainder is 4, so 47 is not a divisor of 2354)
2354 / 48 = 49.041666666667 (the remainder is 2, so 48 is not a divisor of 2354)