What are the divisors of 374?

1, 2, 11, 17, 22, 34, 187, 374

There is a total of 8 positive divisors.
The sum of these divisors is 648.
The arithmetic mean is 81.

4 even divisors

2, 22, 34, 374

4 odd divisors

1, 11, 17, 187

How to compute the divisors of 374?

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 374 by each of the numbers from 1 to 374 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)

374 / 1 = 374 (the remainder is 0, so 1 is a divisor of 374)
374 / 2 = 187 (the remainder is 0, so 2 is a divisor of 374)
374 / 3 = 124.66666666667 (the remainder is 2, so 3 is not a divisor of 374)
...
374 / 373 = 1.0026809651475 (the remainder is 1, so 373 is not a divisor of 374)
374 / 374 = 1 (the remainder is 0, so 374 is a divisor of 374)

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 374 (i.e. 19.339079605814). 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 $\frac{N}{d} = D$ )

374 / 1 = 374 (the remainder is 0, so 1 and 374 are divisors of 374)
374 / 2 = 187 (the remainder is 0, so 2 and 187 are divisors of 374)
374 / 3 = 124.66666666667 (the remainder is 2, so 3 is not a divisor of 374)
...
374 / 18 = 20.777777777778 (the remainder is 14, so 18 is not a divisor of 374)
374 / 19 = 19.684210526316 (the remainder is 13, so 19 is not a divisor of 374)