What are the divisors of 1522?

1, 2, 761, 1522

There is a total of 4 positive divisors.
The sum of these divisors is 2286.
The arithmetic mean is 571.5.

2 even divisors

2, 1522

2 odd divisors

1, 761

How to compute the divisors of 1522?

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 1522 by each of the numbers from 1 to 1522 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)

1522 / 1 = 1522 (the remainder is 0, so 1 is a divisor of 1522)
1522 / 2 = 761 (the remainder is 0, so 2 is a divisor of 1522)
1522 / 3 = 507.33333333333 (the remainder is 1, so 3 is not a divisor of 1522)
...
1522 / 1521 = 1.0006574621959 (the remainder is 1, so 1521 is not a divisor of 1522)
1522 / 1522 = 1 (the remainder is 0, so 1522 is a divisor of 1522)

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 1522 (i.e. 39.012818406262). 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 $\frac{N}{d} = D$ )

1522 / 1 = 1522 (the remainder is 0, so 1 and 1522 are divisors of 1522)
1522 / 2 = 761 (the remainder is 0, so 2 and 761 are divisors of 1522)
1522 / 3 = 507.33333333333 (the remainder is 1, so 3 is not a divisor of 1522)
...
1522 / 38 = 40.052631578947 (the remainder is 2, so 38 is not a divisor of 1522)
1522 / 39 = 39.025641025641 (the remainder is 1, so 39 is not a divisor of 1522)