What are the divisors of 4748?

1, 2, 4, 1187, 2374, 4748

There is a total of 6 positive divisors.
The sum of these divisors is 8316.
The arithmetic mean is 1386.

4 even divisors

2, 4, 2374, 4748

2 odd divisors

1, 1187

How to compute the divisors of 4748?

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 4748 by each of the numbers from 1 to 4748 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)

4748 / 1 = 4748 (the remainder is 0, so 1 is a divisor of 4748)
4748 / 2 = 2374 (the remainder is 0, so 2 is a divisor of 4748)
4748 / 3 = 1582.6666666667 (the remainder is 2, so 3 is not a divisor of 4748)
...
4748 / 4747 = 1.0002106593638 (the remainder is 1, so 4747 is not a divisor of 4748)
4748 / 4748 = 1 (the remainder is 0, so 4748 is a divisor of 4748)

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 4748 (i.e. 68.905732707809). 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 $\frac{N}{d} = D$ )

4748 / 1 = 4748 (the remainder is 0, so 1 and 4748 are divisors of 4748)
4748 / 2 = 2374 (the remainder is 0, so 2 and 2374 are divisors of 4748)
4748 / 3 = 1582.6666666667 (the remainder is 2, so 3 is not a divisor of 4748)
...
4748 / 67 = 70.865671641791 (the remainder is 58, so 67 is not a divisor of 4748)
4748 / 68 = 69.823529411765 (the remainder is 56, so 68 is not a divisor of 4748)