What are the divisors of 7002?

1, 2, 3, 6, 9, 18, 389, 778, 1167, 2334, 3501, 7002

There is a total of 12 positive divisors.
The sum of these divisors is 15210.
The arithmetic mean is 1267.5.

6 even divisors

2, 6, 18, 778, 2334, 7002

6 odd divisors

1, 3, 9, 389, 1167, 3501

How to compute the divisors of 7002?

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 7002 by each of the numbers from 1 to 7002 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)

7002 / 1 = 7002 (the remainder is 0, so 1 is a divisor of 7002)
7002 / 2 = 3501 (the remainder is 0, so 2 is a divisor of 7002)
7002 / 3 = 2334 (the remainder is 0, so 3 is a divisor of 7002)
...
7002 / 7001 = 1.0001428367376 (the remainder is 1, so 7001 is not a divisor of 7002)
7002 / 7002 = 1 (the remainder is 0, so 7002 is a divisor of 7002)

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 7002 (i.e. 83.677954085888). 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 $\frac{N}{d} = D$ )

7002 / 1 = 7002 (the remainder is 0, so 1 and 7002 are divisors of 7002)
7002 / 2 = 3501 (the remainder is 0, so 2 and 3501 are divisors of 7002)
7002 / 3 = 2334 (the remainder is 0, so 3 and 2334 are divisors of 7002)
...
7002 / 82 = 85.390243902439 (the remainder is 32, so 82 is not a divisor of 7002)
7002 / 83 = 84.361445783133 (the remainder is 30, so 83 is not a divisor of 7002)