What are the divisors of 534?

1, 2, 3, 6, 89, 178, 267, 534

There is a total of 8 positive divisors.
The sum of these divisors is 1080.
The arithmetic mean is 135.

4 even divisors

2, 6, 178, 534

4 odd divisors

1, 3, 89, 267

How to compute the divisors of 534?

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 534 by each of the numbers from 1 to 534 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)

534 / 1 = 534 (the remainder is 0, so 1 is a divisor of 534)
534 / 2 = 267 (the remainder is 0, so 2 is a divisor of 534)
534 / 3 = 178 (the remainder is 0, so 3 is a divisor of 534)
...
534 / 533 = 1.0018761726079 (the remainder is 1, so 533 is not a divisor of 534)
534 / 534 = 1 (the remainder is 0, so 534 is a divisor of 534)

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 534 (i.e. 23.108440016583). 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 $\frac{N}{d} = D$ )

534 / 1 = 534 (the remainder is 0, so 1 and 534 are divisors of 534)
534 / 2 = 267 (the remainder is 0, so 2 and 267 are divisors of 534)
534 / 3 = 178 (the remainder is 0, so 3 and 178 are divisors of 534)
...
534 / 22 = 24.272727272727 (the remainder is 6, so 22 is not a divisor of 534)
534 / 23 = 23.217391304348 (the remainder is 5, so 23 is not a divisor of 534)