What are the divisors of 362?

1, 2, 181, 362

There is a total of 4 positive divisors.
The sum of these divisors is 546.
The arithmetic mean is 136.5.

2 even divisors

2, 362

2 odd divisors

1, 181

How to compute the divisors of 362?

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 362 by each of the numbers from 1 to 362 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)

362 / 1 = 362 (the remainder is 0, so 1 is a divisor of 362)
362 / 2 = 181 (the remainder is 0, so 2 is a divisor of 362)
362 / 3 = 120.66666666667 (the remainder is 2, so 3 is not a divisor of 362)
...
362 / 361 = 1.0027700831025 (the remainder is 1, so 361 is not a divisor of 362)
362 / 362 = 1 (the remainder is 0, so 362 is a divisor of 362)

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 362 (i.e. 19.02629759044). 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 $\frac{N}{d} = D$ )

362 / 1 = 362 (the remainder is 0, so 1 and 362 are divisors of 362)
362 / 2 = 181 (the remainder is 0, so 2 and 181 are divisors of 362)
362 / 3 = 120.66666666667 (the remainder is 2, so 3 is not a divisor of 362)
...
362 / 18 = 20.111111111111 (the remainder is 2, so 18 is not a divisor of 362)
362 / 19 = 19.052631578947 (the remainder is 1, so 19 is not a divisor of 362)