What are the divisors of 3153?

1, 3, 1051, 3153

There is a total of 4 positive divisors.
The sum of these divisors is 4208.
The arithmetic mean is 1052.

4 odd divisors

1, 3, 1051, 3153

How to compute the divisors of 3153?

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 3153 by each of the numbers from 1 to 3153 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)

3153 / 1 = 3153 (the remainder is 0, so 1 is a divisor of 3153)
3153 / 2 = 1576.5 (the remainder is 1, so 2 is not a divisor of 3153)
3153 / 3 = 1051 (the remainder is 0, so 3 is a divisor of 3153)
...
3153 / 3152 = 1.0003172588832 (the remainder is 1, so 3152 is not a divisor of 3153)
3153 / 3153 = 1 (the remainder is 0, so 3153 is a divisor of 3153)

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 3153 (i.e. 56.151580565466). 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 $\frac{N}{d} = D$ )

3153 / 1 = 3153 (the remainder is 0, so 1 and 3153 are divisors of 3153)
3153 / 2 = 1576.5 (the remainder is 1, so 2 is not a divisor of 3153)
3153 / 3 = 1051 (the remainder is 0, so 3 and 1051 are divisors of 3153)
...
3153 / 55 = 57.327272727273 (the remainder is 18, so 55 is not a divisor of 3153)
3153 / 56 = 56.303571428571 (the remainder is 17, so 56 is not a divisor of 3153)