What are the divisors of 4477?

1, 11, 37, 121, 407, 4477

There is a total of 6 positive divisors.
The sum of these divisors is 5054.
The arithmetic mean is 842.33333333333.

6 odd divisors

1, 11, 37, 121, 407, 4477

How to compute the divisors of 4477?

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 4477 by each of the numbers from 1 to 4477 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)

4477 / 1 = 4477 (the remainder is 0, so 1 is a divisor of 4477)
4477 / 2 = 2238.5 (the remainder is 1, so 2 is not a divisor of 4477)
4477 / 3 = 1492.3333333333 (the remainder is 1, so 3 is not a divisor of 4477)
...
4477 / 4476 = 1.0002234137623 (the remainder is 1, so 4476 is not a divisor of 4477)
4477 / 4477 = 1 (the remainder is 0, so 4477 is a divisor of 4477)

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 4477 (i.e. 66.91038783328). 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 $\frac{N}{d} = D$ )

4477 / 1 = 4477 (the remainder is 0, so 1 and 4477 are divisors of 4477)
4477 / 2 = 2238.5 (the remainder is 1, so 2 is not a divisor of 4477)
4477 / 3 = 1492.3333333333 (the remainder is 1, so 3 is not a divisor of 4477)
...
4477 / 65 = 68.876923076923 (the remainder is 57, so 65 is not a divisor of 4477)
4477 / 66 = 67.833333333333 (the remainder is 55, so 66 is not a divisor of 4477)