What are the divisors of 3528?

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 49, 56, 63, 72, 84, 98, 126, 147, 168, 196, 252, 294, 392, 441, 504, 588, 882, 1176, 1764, 3528

There is a total of 36 positive divisors.
The sum of these divisors is 11115.
The arithmetic mean is 308.75.

27 even divisors

2, 4, 6, 8, 12, 14, 18, 24, 28, 36, 42, 56, 72, 84, 98, 126, 168, 196, 252, 294, 392, 504, 588, 882, 1176, 1764, 3528

9 odd divisors

1, 3, 7, 9, 21, 49, 63, 147, 441

How to compute the divisors of 3528?

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 3528 by each of the numbers from 1 to 3528 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)

3528 / 1 = 3528 (the remainder is 0, so 1 is a divisor of 3528)
3528 / 2 = 1764 (the remainder is 0, so 2 is a divisor of 3528)
3528 / 3 = 1176 (the remainder is 0, so 3 is a divisor of 3528)
...
3528 / 3527 = 1.0002835270768 (the remainder is 1, so 3527 is not a divisor of 3528)
3528 / 3528 = 1 (the remainder is 0, so 3528 is a divisor of 3528)

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 3528 (i.e. 59.39696961967). 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 $\frac{N}{d} = D$ )

3528 / 1 = 3528 (the remainder is 0, so 1 and 3528 are divisors of 3528)
3528 / 2 = 1764 (the remainder is 0, so 2 and 1764 are divisors of 3528)
3528 / 3 = 1176 (the remainder is 0, so 3 and 1176 are divisors of 3528)
...
3528 / 58 = 60.827586206897 (the remainder is 48, so 58 is not a divisor of 3528)
3528 / 59 = 59.796610169492 (the remainder is 47, so 59 is not a divisor of 3528)