What are the divisors of 1481?

1, 1481

There is a total of 2 positive divisors.
The sum of these divisors is 1482.
The arithmetic mean is 741.

2 odd divisors

1, 1481

How to compute the divisors of 1481?

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 1481 by each of the numbers from 1 to 1481 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)

1481 / 1 = 1481 (the remainder is 0, so 1 is a divisor of 1481)
1481 / 2 = 740.5 (the remainder is 1, so 2 is not a divisor of 1481)
1481 / 3 = 493.66666666667 (the remainder is 2, so 3 is not a divisor of 1481)
...
1481 / 1480 = 1.0006756756757 (the remainder is 1, so 1480 is not a divisor of 1481)
1481 / 1481 = 1 (the remainder is 0, so 1481 is a divisor of 1481)

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 1481 (i.e. 38.483762809788). 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 $\frac{N}{d} = D$ )

1481 / 1 = 1481 (the remainder is 0, so 1 and 1481 are divisors of 1481)
1481 / 2 = 740.5 (the remainder is 1, so 2 is not a divisor of 1481)
1481 / 3 = 493.66666666667 (the remainder is 2, so 3 is not a divisor of 1481)
...
1481 / 37 = 40.027027027027 (the remainder is 1, so 37 is not a divisor of 1481)
1481 / 38 = 38.973684210526 (the remainder is 37, so 38 is not a divisor of 1481)