What are the divisors of 3513?

1, 3, 1171, 3513

There is a total of 4 positive divisors.
The sum of these divisors is 4688.
The arithmetic mean is 1172.

4 odd divisors

1, 3, 1171, 3513

How to compute the divisors of 3513?

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 3513 by each of the numbers from 1 to 3513 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)

3513 / 1 = 3513 (the remainder is 0, so 1 is a divisor of 3513)
3513 / 2 = 1756.5 (the remainder is 1, so 2 is not a divisor of 3513)
3513 / 3 = 1171 (the remainder is 0, so 3 is a divisor of 3513)
...
3513 / 3512 = 1.000284738041 (the remainder is 1, so 3512 is not a divisor of 3513)
3513 / 3513 = 1 (the remainder is 0, so 3513 is a divisor of 3513)

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 3513 (i.e. 59.27056605095). 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 $\frac{N}{d} = D$ )

3513 / 1 = 3513 (the remainder is 0, so 1 and 3513 are divisors of 3513)
3513 / 2 = 1756.5 (the remainder is 1, so 2 is not a divisor of 3513)
3513 / 3 = 1171 (the remainder is 0, so 3 and 1171 are divisors of 3513)
...
3513 / 58 = 60.568965517241 (the remainder is 33, so 58 is not a divisor of 3513)
3513 / 59 = 59.542372881356 (the remainder is 32, so 59 is not a divisor of 3513)