What are the divisors of 2477?

1, 2477

There is a total of 2 positive divisors.
The sum of these divisors is 2478.
The arithmetic mean is 1239.

2 odd divisors

1, 2477

How to compute the divisors of 2477?

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 2477 by each of the numbers from 1 to 2477 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)

2477 / 1 = 2477 (the remainder is 0, so 1 is a divisor of 2477)
2477 / 2 = 1238.5 (the remainder is 1, so 2 is not a divisor of 2477)
2477 / 3 = 825.66666666667 (the remainder is 2, so 3 is not a divisor of 2477)
...
2477 / 2476 = 1.0004038772213 (the remainder is 1, so 2476 is not a divisor of 2477)
2477 / 2477 = 1 (the remainder is 0, so 2477 is a divisor of 2477)

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 2477 (i.e. 49.769468552517). 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 $\frac{N}{d} = D$ )

2477 / 1 = 2477 (the remainder is 0, so 1 and 2477 are divisors of 2477)
2477 / 2 = 1238.5 (the remainder is 1, so 2 is not a divisor of 2477)
2477 / 3 = 825.66666666667 (the remainder is 2, so 3 is not a divisor of 2477)
...
2477 / 48 = 51.604166666667 (the remainder is 29, so 48 is not a divisor of 2477)
2477 / 49 = 50.551020408163 (the remainder is 27, so 49 is not a divisor of 2477)