What are the divisors of 1402?

1, 2, 701, 1402

There is a total of 4 positive divisors.
The sum of these divisors is 2106.
The arithmetic mean is 526.5.

2 even divisors

2, 1402

2 odd divisors

1, 701

How to compute the divisors of 1402?

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 1402 by each of the numbers from 1 to 1402 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)

1402 / 1 = 1402 (the remainder is 0, so 1 is a divisor of 1402)
1402 / 2 = 701 (the remainder is 0, so 2 is a divisor of 1402)
1402 / 3 = 467.33333333333 (the remainder is 1, so 3 is not a divisor of 1402)
...
1402 / 1401 = 1.0007137758744 (the remainder is 1, so 1401 is not a divisor of 1402)
1402 / 1402 = 1 (the remainder is 0, so 1402 is a divisor of 1402)

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 1402 (i.e. 37.443290453698). 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 $\frac{N}{d} = D$ )

1402 / 1 = 1402 (the remainder is 0, so 1 and 1402 are divisors of 1402)
1402 / 2 = 701 (the remainder is 0, so 2 and 701 are divisors of 1402)
1402 / 3 = 467.33333333333 (the remainder is 1, so 3 is not a divisor of 1402)
...
1402 / 36 = 38.944444444444 (the remainder is 34, so 36 is not a divisor of 1402)
1402 / 37 = 37.891891891892 (the remainder is 33, so 37 is not a divisor of 1402)