What are the divisors of 4932?

1, 2, 3, 4, 6, 9, 12, 18, 36, 137, 274, 411, 548, 822, 1233, 1644, 2466, 4932

There is a total of 18 positive divisors.
The sum of these divisors is 12558.
The arithmetic mean is 697.66666666667.

12 even divisors

2, 4, 6, 12, 18, 36, 274, 548, 822, 1644, 2466, 4932

6 odd divisors

1, 3, 9, 137, 411, 1233

How to compute the divisors of 4932?

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 4932 by each of the numbers from 1 to 4932 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)

4932 / 1 = 4932 (the remainder is 0, so 1 is a divisor of 4932)
4932 / 2 = 2466 (the remainder is 0, so 2 is a divisor of 4932)
4932 / 3 = 1644 (the remainder is 0, so 3 is a divisor of 4932)
...
4932 / 4931 = 1.000202798621 (the remainder is 1, so 4931 is not a divisor of 4932)
4932 / 4932 = 1 (the remainder is 0, so 4932 is a divisor of 4932)

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 4932 (i.e. 70.228199464318). 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 $\frac{N}{d} = D$ )

4932 / 1 = 4932 (the remainder is 0, so 1 and 4932 are divisors of 4932)
4932 / 2 = 2466 (the remainder is 0, so 2 and 2466 are divisors of 4932)
4932 / 3 = 1644 (the remainder is 0, so 3 and 1644 are divisors of 4932)
...
4932 / 69 = 71.478260869565 (the remainder is 33, so 69 is not a divisor of 4932)
4932 / 70 = 70.457142857143 (the remainder is 32, so 70 is not a divisor of 4932)