What are the divisors of 964?

1, 2, 4, 241, 482, 964

There is a total of 6 positive divisors.
The sum of these divisors is 1694.
The arithmetic mean is 282.33333333333.

4 even divisors

2, 4, 482, 964

2 odd divisors

1, 241

How to compute the divisors of 964?

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 964 by each of the numbers from 1 to 964 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)

964 / 1 = 964 (the remainder is 0, so 1 is a divisor of 964)
964 / 2 = 482 (the remainder is 0, so 2 is a divisor of 964)
964 / 3 = 321.33333333333 (the remainder is 1, so 3 is not a divisor of 964)
...
964 / 963 = 1.0010384215992 (the remainder is 1, so 963 is not a divisor of 964)
964 / 964 = 1 (the remainder is 0, so 964 is a divisor of 964)

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 964 (i.e. 31.04834939252). 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 $\frac{N}{d} = D$ )

964 / 1 = 964 (the remainder is 0, so 1 and 964 are divisors of 964)
964 / 2 = 482 (the remainder is 0, so 2 and 482 are divisors of 964)
964 / 3 = 321.33333333333 (the remainder is 1, so 3 is not a divisor of 964)
...
964 / 30 = 32.133333333333 (the remainder is 4, so 30 is not a divisor of 964)
964 / 31 = 31.096774193548 (the remainder is 3, so 31 is not a divisor of 964)