What are the divisors of 370?

1, 2, 5, 10, 37, 74, 185, 370

There is a total of 8 positive divisors.
The sum of these divisors is 684.
The arithmetic mean is 85.5.

4 even divisors

2, 10, 74, 370

4 odd divisors

1, 5, 37, 185

How to compute the divisors of 370?

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 370 by each of the numbers from 1 to 370 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)

370 / 1 = 370 (the remainder is 0, so 1 is a divisor of 370)
370 / 2 = 185 (the remainder is 0, so 2 is a divisor of 370)
370 / 3 = 123.33333333333 (the remainder is 1, so 3 is not a divisor of 370)
...
370 / 369 = 1.0027100271003 (the remainder is 1, so 369 is not a divisor of 370)
370 / 370 = 1 (the remainder is 0, so 370 is a divisor of 370)

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 370 (i.e. 19.235384061671). 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 $\frac{N}{d} = D$ )

370 / 1 = 370 (the remainder is 0, so 1 and 370 are divisors of 370)
370 / 2 = 185 (the remainder is 0, so 2 and 185 are divisors of 370)
370 / 3 = 123.33333333333 (the remainder is 1, so 3 is not a divisor of 370)
...
370 / 18 = 20.555555555556 (the remainder is 10, so 18 is not a divisor of 370)
370 / 19 = 19.473684210526 (the remainder is 9, so 19 is not a divisor of 370)