What are the divisors of 4962?

1, 2, 3, 6, 827, 1654, 2481, 4962

There is a total of 8 positive divisors.
The sum of these divisors is 9936.
The arithmetic mean is 1242.

4 even divisors

2, 6, 1654, 4962

4 odd divisors

1, 3, 827, 2481

How to compute the divisors of 4962?

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 4962 by each of the numbers from 1 to 4962 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)

4962 / 1 = 4962 (the remainder is 0, so 1 is a divisor of 4962)
4962 / 2 = 2481 (the remainder is 0, so 2 is a divisor of 4962)
4962 / 3 = 1654 (the remainder is 0, so 3 is a divisor of 4962)
...
4962 / 4961 = 1.0002015722637 (the remainder is 1, so 4961 is not a divisor of 4962)
4962 / 4962 = 1 (the remainder is 0, so 4962 is a divisor of 4962)

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 4962 (i.e. 70.441465061425). 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 $\frac{N}{d} = D$ )

4962 / 1 = 4962 (the remainder is 0, so 1 and 4962 are divisors of 4962)
4962 / 2 = 2481 (the remainder is 0, so 2 and 2481 are divisors of 4962)
4962 / 3 = 1654 (the remainder is 0, so 3 and 1654 are divisors of 4962)
...
4962 / 69 = 71.913043478261 (the remainder is 63, so 69 is not a divisor of 4962)
4962 / 70 = 70.885714285714 (the remainder is 62, so 70 is not a divisor of 4962)