What are the divisors of 2474?

1, 2, 1237, 2474

There is a total of 4 positive divisors.
The sum of these divisors is 3714.
The arithmetic mean is 928.5.

2 even divisors

2, 2474

2 odd divisors

1, 1237

How to compute the divisors of 2474?

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 2474 by each of the numbers from 1 to 2474 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)

2474 / 1 = 2474 (the remainder is 0, so 1 is a divisor of 2474)
2474 / 2 = 1237 (the remainder is 0, so 2 is a divisor of 2474)
2474 / 3 = 824.66666666667 (the remainder is 2, so 3 is not a divisor of 2474)
...
2474 / 2473 = 1.0004043671654 (the remainder is 1, so 2473 is not a divisor of 2474)
2474 / 2474 = 1 (the remainder is 0, so 2474 is a divisor of 2474)

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 2474 (i.e. 49.739320461784). 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 $\frac{N}{d} = D$ )

2474 / 1 = 2474 (the remainder is 0, so 1 and 2474 are divisors of 2474)
2474 / 2 = 1237 (the remainder is 0, so 2 and 1237 are divisors of 2474)
2474 / 3 = 824.66666666667 (the remainder is 2, so 3 is not a divisor of 2474)
...
2474 / 48 = 51.541666666667 (the remainder is 26, so 48 is not a divisor of 2474)
2474 / 49 = 50.489795918367 (the remainder is 24, so 49 is not a divisor of 2474)