What are the divisors of 4977?

1, 3, 7, 9, 21, 63, 79, 237, 553, 711, 1659, 4977

There is a total of 12 positive divisors.
The sum of these divisors is 8320.
The arithmetic mean is 693.33333333333.

12 odd divisors

1, 3, 7, 9, 21, 63, 79, 237, 553, 711, 1659, 4977

How to compute the divisors of 4977?

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 4977 by each of the numbers from 1 to 4977 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)

4977 / 1 = 4977 (the remainder is 0, so 1 is a divisor of 4977)
4977 / 2 = 2488.5 (the remainder is 1, so 2 is not a divisor of 4977)
4977 / 3 = 1659 (the remainder is 0, so 3 is a divisor of 4977)
...
4977 / 4976 = 1.0002009646302 (the remainder is 1, so 4976 is not a divisor of 4977)
4977 / 4977 = 1 (the remainder is 0, so 4977 is a divisor of 4977)

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 4977 (i.e. 70.547856097829). 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 $\frac{N}{d} = D$ )

4977 / 1 = 4977 (the remainder is 0, so 1 and 4977 are divisors of 4977)
4977 / 2 = 2488.5 (the remainder is 1, so 2 is not a divisor of 4977)
4977 / 3 = 1659 (the remainder is 0, so 3 and 1659 are divisors of 4977)
...
4977 / 69 = 72.130434782609 (the remainder is 9, so 69 is not a divisor of 4977)
4977 / 70 = 71.1 (the remainder is 7, so 70 is not a divisor of 4977)