What are the divisors of 7053?

1, 3, 2351, 7053

There is a total of 4 positive divisors.
The sum of these divisors is 9408.
The arithmetic mean is 2352.

4 odd divisors

1, 3, 2351, 7053

How to compute the divisors of 7053?

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 7053 by each of the numbers from 1 to 7053 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)

7053 / 1 = 7053 (the remainder is 0, so 1 is a divisor of 7053)
7053 / 2 = 3526.5 (the remainder is 1, so 2 is not a divisor of 7053)
7053 / 3 = 2351 (the remainder is 0, so 3 is a divisor of 7053)
...
7053 / 7052 = 1.0001418037436 (the remainder is 1, so 7052 is not a divisor of 7053)
7053 / 7053 = 1 (the remainder is 0, so 7053 is a divisor of 7053)

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 7053 (i.e. 83.982140958659). 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 $\frac{N}{d} = D$ )

7053 / 1 = 7053 (the remainder is 0, so 1 and 7053 are divisors of 7053)
7053 / 2 = 3526.5 (the remainder is 1, so 2 is not a divisor of 7053)
7053 / 3 = 2351 (the remainder is 0, so 3 and 2351 are divisors of 7053)
...
7053 / 82 = 86.012195121951 (the remainder is 1, so 82 is not a divisor of 7053)
7053 / 83 = 84.975903614458 (the remainder is 81, so 83 is not a divisor of 7053)