What are the divisors of 2402?

1, 2, 1201, 2402

There is a total of 4 positive divisors.
The sum of these divisors is 3606.
The arithmetic mean is 901.5.

2 even divisors

2, 2402

2 odd divisors

1, 1201

How to compute the divisors of 2402?

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 2402 by each of the numbers from 1 to 2402 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)

2402 / 1 = 2402 (the remainder is 0, so 1 is a divisor of 2402)
2402 / 2 = 1201 (the remainder is 0, so 2 is a divisor of 2402)
2402 / 3 = 800.66666666667 (the remainder is 2, so 3 is not a divisor of 2402)
...
2402 / 2401 = 1.0004164931279 (the remainder is 1, so 2401 is not a divisor of 2402)
2402 / 2402 = 1 (the remainder is 0, so 2402 is a divisor of 2402)

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 2402 (i.e. 49.010203019371). 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 $\frac{N}{d} = D$ )

2402 / 1 = 2402 (the remainder is 0, so 1 and 2402 are divisors of 2402)
2402 / 2 = 1201 (the remainder is 0, so 2 and 1201 are divisors of 2402)
2402 / 3 = 800.66666666667 (the remainder is 2, so 3 is not a divisor of 2402)
...
2402 / 48 = 50.041666666667 (the remainder is 2, so 48 is not a divisor of 2402)
2402 / 49 = 49.020408163265 (the remainder is 1, so 49 is not a divisor of 2402)