What are the divisors of 4700?

1, 2, 4, 5, 10, 20, 25, 47, 50, 94, 100, 188, 235, 470, 940, 1175, 2350, 4700

There is a total of 18 positive divisors.
The sum of these divisors is 10416.
The arithmetic mean is 578.66666666667.

12 even divisors

2, 4, 10, 20, 50, 94, 100, 188, 470, 940, 2350, 4700

6 odd divisors

1, 5, 25, 47, 235, 1175

How to compute the divisors of 4700?

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 4700 by each of the numbers from 1 to 4700 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)

4700 / 1 = 4700 (the remainder is 0, so 1 is a divisor of 4700)
4700 / 2 = 2350 (the remainder is 0, so 2 is a divisor of 4700)
4700 / 3 = 1566.6666666667 (the remainder is 2, so 3 is not a divisor of 4700)
...
4700 / 4699 = 1.0002128112364 (the remainder is 1, so 4699 is not a divisor of 4700)
4700 / 4700 = 1 (the remainder is 0, so 4700 is a divisor of 4700)

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 4700 (i.e. 68.55654600401). 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 $\frac{N}{d} = D$ )

4700 / 1 = 4700 (the remainder is 0, so 1 and 4700 are divisors of 4700)
4700 / 2 = 2350 (the remainder is 0, so 2 and 2350 are divisors of 4700)
4700 / 3 = 1566.6666666667 (the remainder is 2, so 3 is not a divisor of 4700)
...
4700 / 67 = 70.149253731343 (the remainder is 10, so 67 is not a divisor of 4700)
4700 / 68 = 69.117647058824 (the remainder is 8, so 68 is not a divisor of 4700)