What are the divisors of 481?

1, 13, 37, 481

There is a total of 4 positive divisors.
The sum of these divisors is 532.
The arithmetic mean is 133.

4 odd divisors

1, 13, 37, 481

How to compute the divisors of 481?

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 481 by each of the numbers from 1 to 481 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)

481 / 1 = 481 (the remainder is 0, so 1 is a divisor of 481)
481 / 2 = 240.5 (the remainder is 1, so 2 is not a divisor of 481)
481 / 3 = 160.33333333333 (the remainder is 1, so 3 is not a divisor of 481)
...
481 / 480 = 1.0020833333333 (the remainder is 1, so 480 is not a divisor of 481)
481 / 481 = 1 (the remainder is 0, so 481 is a divisor of 481)

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 481 (i.e. 21.931712199461). 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 $\frac{N}{d} = D$ )

481 / 1 = 481 (the remainder is 0, so 1 and 481 are divisors of 481)
481 / 2 = 240.5 (the remainder is 1, so 2 is not a divisor of 481)
481 / 3 = 160.33333333333 (the remainder is 1, so 3 is not a divisor of 481)
...
481 / 20 = 24.05 (the remainder is 1, so 20 is not a divisor of 481)
481 / 21 = 22.904761904762 (the remainder is 19, so 21 is not a divisor of 481)