What are the divisors of 962?

1, 2, 13, 26, 37, 74, 481, 962

There is a total of 8 positive divisors.
The sum of these divisors is 1596.
The arithmetic mean is 199.5.

4 even divisors

2, 26, 74, 962

4 odd divisors

1, 13, 37, 481

How to compute the divisors of 962?

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 962 by each of the numbers from 1 to 962 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)

962 / 1 = 962 (the remainder is 0, so 1 is a divisor of 962)
962 / 2 = 481 (the remainder is 0, so 2 is a divisor of 962)
962 / 3 = 320.66666666667 (the remainder is 2, so 3 is not a divisor of 962)
...
962 / 961 = 1.0010405827263 (the remainder is 1, so 961 is not a divisor of 962)
962 / 962 = 1 (the remainder is 0, so 962 is a divisor of 962)

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 962 (i.e. 31.016124838542). 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 $\frac{N}{d} = D$ )

962 / 1 = 962 (the remainder is 0, so 1 and 962 are divisors of 962)
962 / 2 = 481 (the remainder is 0, so 2 and 481 are divisors of 962)
962 / 3 = 320.66666666667 (the remainder is 2, so 3 is not a divisor of 962)
...
962 / 30 = 32.066666666667 (the remainder is 2, so 30 is not a divisor of 962)
962 / 31 = 31.032258064516 (the remainder is 1, so 31 is not a divisor of 962)