What are the divisors of 1322?

1, 2, 661, 1322

There is a total of 4 positive divisors.
The sum of these divisors is 1986.
The arithmetic mean is 496.5.

2 even divisors

2, 1322

2 odd divisors

1, 661

How to compute the divisors of 1322?

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 1322 by each of the numbers from 1 to 1322 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)

1322 / 1 = 1322 (the remainder is 0, so 1 is a divisor of 1322)
1322 / 2 = 661 (the remainder is 0, so 2 is a divisor of 1322)
1322 / 3 = 440.66666666667 (the remainder is 2, so 3 is not a divisor of 1322)
...
1322 / 1321 = 1.000757002271 (the remainder is 1, so 1321 is not a divisor of 1322)
1322 / 1322 = 1 (the remainder is 0, so 1322 is a divisor of 1322)

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 1322 (i.e. 36.359317925396). 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 $\frac{N}{d} = D$ )

1322 / 1 = 1322 (the remainder is 0, so 1 and 1322 are divisors of 1322)
1322 / 2 = 661 (the remainder is 0, so 2 and 661 are divisors of 1322)
1322 / 3 = 440.66666666667 (the remainder is 2, so 3 is not a divisor of 1322)
...
1322 / 35 = 37.771428571429 (the remainder is 27, so 35 is not a divisor of 1322)
1322 / 36 = 36.722222222222 (the remainder is 26, so 36 is not a divisor of 1322)