What are the divisors of 4370?

1, 2, 5, 10, 19, 23, 38, 46, 95, 115, 190, 230, 437, 874, 2185, 4370

There is a total of 16 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 540.

8 even divisors

2, 10, 38, 46, 190, 230, 874, 4370

8 odd divisors

1, 5, 19, 23, 95, 115, 437, 2185

How to compute the divisors of 4370?

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 4370 by each of the numbers from 1 to 4370 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)

4370 / 1 = 4370 (the remainder is 0, so 1 is a divisor of 4370)
4370 / 2 = 2185 (the remainder is 0, so 2 is a divisor of 4370)
4370 / 3 = 1456.6666666667 (the remainder is 2, so 3 is not a divisor of 4370)
...
4370 / 4369 = 1.0002288853285 (the remainder is 1, so 4369 is not a divisor of 4370)
4370 / 4370 = 1 (the remainder is 0, so 4370 is a divisor of 4370)

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 4370 (i.e. 66.105975524154). 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 $\frac{N}{d} = D$ )

4370 / 1 = 4370 (the remainder is 0, so 1 and 4370 are divisors of 4370)
4370 / 2 = 2185 (the remainder is 0, so 2 and 2185 are divisors of 4370)
4370 / 3 = 1456.6666666667 (the remainder is 2, so 3 is not a divisor of 4370)
...
4370 / 65 = 67.230769230769 (the remainder is 15, so 65 is not a divisor of 4370)
4370 / 66 = 66.212121212121 (the remainder is 14, so 66 is not a divisor of 4370)