What are the divisors of 4956?

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 59, 84, 118, 177, 236, 354, 413, 708, 826, 1239, 1652, 2478, 4956

There is a total of 24 positive divisors.
The sum of these divisors is 13440.
The arithmetic mean is 560.

16 even divisors

2, 4, 6, 12, 14, 28, 42, 84, 118, 236, 354, 708, 826, 1652, 2478, 4956

8 odd divisors

1, 3, 7, 21, 59, 177, 413, 1239

How to compute the divisors of 4956?

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 4956 by each of the numbers from 1 to 4956 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)

4956 / 1 = 4956 (the remainder is 0, so 1 is a divisor of 4956)
4956 / 2 = 2478 (the remainder is 0, so 2 is a divisor of 4956)
4956 / 3 = 1652 (the remainder is 0, so 3 is a divisor of 4956)
...
4956 / 4955 = 1.0002018163471 (the remainder is 1, so 4955 is not a divisor of 4956)
4956 / 4956 = 1 (the remainder is 0, so 4956 is a divisor of 4956)

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 4956 (i.e. 70.398863627192). 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 $\frac{N}{d} = D$ )

4956 / 1 = 4956 (the remainder is 0, so 1 and 4956 are divisors of 4956)
4956 / 2 = 2478 (the remainder is 0, so 2 and 2478 are divisors of 4956)
4956 / 3 = 1652 (the remainder is 0, so 3 and 1652 are divisors of 4956)
...
4956 / 69 = 71.826086956522 (the remainder is 57, so 69 is not a divisor of 4956)
4956 / 70 = 70.8 (the remainder is 56, so 70 is not a divisor of 4956)