What are the divisors of 4967?

1, 4967

There is a total of 2 positive divisors.
The sum of these divisors is 4968.
The arithmetic mean is 2484.

2 odd divisors

1, 4967

How to compute the divisors of 4967?

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 4967 by each of the numbers from 1 to 4967 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)

4967 / 1 = 4967 (the remainder is 0, so 1 is a divisor of 4967)
4967 / 2 = 2483.5 (the remainder is 1, so 2 is not a divisor of 4967)
4967 / 3 = 1655.6666666667 (the remainder is 2, so 3 is not a divisor of 4967)
...
4967 / 4966 = 1.0002013693113 (the remainder is 1, so 4966 is not a divisor of 4967)
4967 / 4967 = 1 (the remainder is 0, so 4967 is a divisor of 4967)

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 4967 (i.e. 70.476946585391). 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 $\frac{N}{d} = D$ )

4967 / 1 = 4967 (the remainder is 0, so 1 and 4967 are divisors of 4967)
4967 / 2 = 2483.5 (the remainder is 1, so 2 is not a divisor of 4967)
4967 / 3 = 1655.6666666667 (the remainder is 2, so 3 is not a divisor of 4967)
...
4967 / 69 = 71.985507246377 (the remainder is 68, so 69 is not a divisor of 4967)
4967 / 70 = 70.957142857143 (the remainder is 67, so 70 is not a divisor of 4967)