What are the divisors of 373?

1, 373

There is a total of 2 positive divisors.
The sum of these divisors is 374.
The arithmetic mean is 187.

2 odd divisors

1, 373

How to compute the divisors of 373?

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 373 by each of the numbers from 1 to 373 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)

373 / 1 = 373 (the remainder is 0, so 1 is a divisor of 373)
373 / 2 = 186.5 (the remainder is 1, so 2 is not a divisor of 373)
373 / 3 = 124.33333333333 (the remainder is 1, so 3 is not a divisor of 373)
...
373 / 372 = 1.002688172043 (the remainder is 1, so 372 is not a divisor of 373)
373 / 373 = 1 (the remainder is 0, so 373 is a divisor of 373)

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 373 (i.e. 19.313207915828). 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 $\frac{N}{d} = D$ )

373 / 1 = 373 (the remainder is 0, so 1 and 373 are divisors of 373)
373 / 2 = 186.5 (the remainder is 1, so 2 is not a divisor of 373)
373 / 3 = 124.33333333333 (the remainder is 1, so 3 is not a divisor of 373)
...
373 / 18 = 20.722222222222 (the remainder is 13, so 18 is not a divisor of 373)
373 / 19 = 19.631578947368 (the remainder is 12, so 19 is not a divisor of 373)