What are the divisors of 1283?

1, 1283

There is a total of 2 positive divisors.
The sum of these divisors is 1284.
The arithmetic mean is 642.

2 odd divisors

1, 1283

How to compute the divisors of 1283?

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 1283 by each of the numbers from 1 to 1283 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)

1283 / 1 = 1283 (the remainder is 0, so 1 is a divisor of 1283)
1283 / 2 = 641.5 (the remainder is 1, so 2 is not a divisor of 1283)
1283 / 3 = 427.66666666667 (the remainder is 2, so 3 is not a divisor of 1283)
...
1283 / 1282 = 1.0007800312012 (the remainder is 1, so 1282 is not a divisor of 1283)
1283 / 1283 = 1 (the remainder is 0, so 1283 is a divisor of 1283)

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 1283 (i.e. 35.818989377145). 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 $\frac{N}{d} = D$ )

1283 / 1 = 1283 (the remainder is 0, so 1 and 1283 are divisors of 1283)
1283 / 2 = 641.5 (the remainder is 1, so 2 is not a divisor of 1283)
1283 / 3 = 427.66666666667 (the remainder is 2, so 3 is not a divisor of 1283)
...
1283 / 34 = 37.735294117647 (the remainder is 25, so 34 is not a divisor of 1283)
1283 / 35 = 36.657142857143 (the remainder is 23, so 35 is not a divisor of 1283)