What are the divisors of 1486?

1, 2, 743, 1486

There is a total of 4 positive divisors.
The sum of these divisors is 2232.
The arithmetic mean is 558.

2 even divisors

2, 1486

2 odd divisors

1, 743

How to compute the divisors of 1486?

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 1486 by each of the numbers from 1 to 1486 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)

1486 / 1 = 1486 (the remainder is 0, so 1 is a divisor of 1486)
1486 / 2 = 743 (the remainder is 0, so 2 is a divisor of 1486)
1486 / 3 = 495.33333333333 (the remainder is 1, so 3 is not a divisor of 1486)
...
1486 / 1485 = 1.0006734006734 (the remainder is 1, so 1485 is not a divisor of 1486)
1486 / 1486 = 1 (the remainder is 0, so 1486 is a divisor of 1486)

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 1486 (i.e. 38.548670534793). 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 $\frac{N}{d} = D$ )

1486 / 1 = 1486 (the remainder is 0, so 1 and 1486 are divisors of 1486)
1486 / 2 = 743 (the remainder is 0, so 2 and 743 are divisors of 1486)
1486 / 3 = 495.33333333333 (the remainder is 1, so 3 is not a divisor of 1486)
...
1486 / 37 = 40.162162162162 (the remainder is 6, so 37 is not a divisor of 1486)
1486 / 38 = 39.105263157895 (the remainder is 4, so 38 is not a divisor of 1486)