What are the divisors of 4376?

1, 2, 4, 8, 547, 1094, 2188, 4376

There is a total of 8 positive divisors.
The sum of these divisors is 8220.
The arithmetic mean is 1027.5.

6 even divisors

2, 4, 8, 1094, 2188, 4376

2 odd divisors

1, 547

How to compute the divisors of 4376?

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 4376 by each of the numbers from 1 to 4376 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)

4376 / 1 = 4376 (the remainder is 0, so 1 is a divisor of 4376)
4376 / 2 = 2188 (the remainder is 0, so 2 is a divisor of 4376)
4376 / 3 = 1458.6666666667 (the remainder is 2, so 3 is not a divisor of 4376)
...
4376 / 4375 = 1.0002285714286 (the remainder is 1, so 4375 is not a divisor of 4376)
4376 / 4376 = 1 (the remainder is 0, so 4376 is a divisor of 4376)

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 4376 (i.e. 66.151341634165). 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 $\frac{N}{d} = D$ )

4376 / 1 = 4376 (the remainder is 0, so 1 and 4376 are divisors of 4376)
4376 / 2 = 2188 (the remainder is 0, so 2 and 2188 are divisors of 4376)
4376 / 3 = 1458.6666666667 (the remainder is 2, so 3 is not a divisor of 4376)
...
4376 / 65 = 67.323076923077 (the remainder is 21, so 65 is not a divisor of 4376)
4376 / 66 = 66.30303030303 (the remainder is 20, so 66 is not a divisor of 4376)