What are the divisors of 4969?

1, 4969

There is a total of 2 positive divisors.
The sum of these divisors is 4970.
The arithmetic mean is 2485.

2 odd divisors

1, 4969

How to compute the divisors of 4969?

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 4969 by each of the numbers from 1 to 4969 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)

4969 / 1 = 4969 (the remainder is 0, so 1 is a divisor of 4969)
4969 / 2 = 2484.5 (the remainder is 1, so 2 is not a divisor of 4969)
4969 / 3 = 1656.3333333333 (the remainder is 1, so 3 is not a divisor of 4969)
...
4969 / 4968 = 1.0002012882448 (the remainder is 1, so 4968 is not a divisor of 4969)
4969 / 4969 = 1 (the remainder is 0, so 4969 is a divisor of 4969)

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 4969 (i.e. 70.491134194308). 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 $\frac{N}{d} = D$ )

4969 / 1 = 4969 (the remainder is 0, so 1 and 4969 are divisors of 4969)
4969 / 2 = 2484.5 (the remainder is 1, so 2 is not a divisor of 4969)
4969 / 3 = 1656.3333333333 (the remainder is 1, so 3 is not a divisor of 4969)
...
4969 / 69 = 72.014492753623 (the remainder is 1, so 69 is not a divisor of 4969)
4969 / 70 = 70.985714285714 (the remainder is 69, so 70 is not a divisor of 4969)