What are the divisors of 4924?

1, 2, 4, 1231, 2462, 4924

There is a total of 6 positive divisors.
The sum of these divisors is 8624.
The arithmetic mean is 1437.3333333333.

4 even divisors

2, 4, 2462, 4924

2 odd divisors

1, 1231

How to compute the divisors of 4924?

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 4924 by each of the numbers from 1 to 4924 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)

4924 / 1 = 4924 (the remainder is 0, so 1 is a divisor of 4924)
4924 / 2 = 2462 (the remainder is 0, so 2 is a divisor of 4924)
4924 / 3 = 1641.3333333333 (the remainder is 1, so 3 is not a divisor of 4924)
...
4924 / 4923 = 1.0002031281739 (the remainder is 1, so 4923 is not a divisor of 4924)
4924 / 4924 = 1 (the remainder is 0, so 4924 is a divisor of 4924)

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 4924 (i.e. 70.171219171395). 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 $\frac{N}{d} = D$ )

4924 / 1 = 4924 (the remainder is 0, so 1 and 4924 are divisors of 4924)
4924 / 2 = 2462 (the remainder is 0, so 2 and 2462 are divisors of 4924)
4924 / 3 = 1641.3333333333 (the remainder is 1, so 3 is not a divisor of 4924)
...
4924 / 69 = 71.36231884058 (the remainder is 25, so 69 is not a divisor of 4924)
4924 / 70 = 70.342857142857 (the remainder is 24, so 70 is not a divisor of 4924)