What are the divisors of 4760?

1, 2, 4, 5, 7, 8, 10, 14, 17, 20, 28, 34, 35, 40, 56, 68, 70, 85, 119, 136, 140, 170, 238, 280, 340, 476, 595, 680, 952, 1190, 2380, 4760

There is a total of 32 positive divisors.
The sum of these divisors is 12960.
The arithmetic mean is 405.

24 even divisors

2, 4, 8, 10, 14, 20, 28, 34, 40, 56, 68, 70, 136, 140, 170, 238, 280, 340, 476, 680, 952, 1190, 2380, 4760

8 odd divisors

1, 5, 7, 17, 35, 85, 119, 595

How to compute the divisors of 4760?

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 4760 by each of the numbers from 1 to 4760 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)

4760 / 1 = 4760 (the remainder is 0, so 1 is a divisor of 4760)
4760 / 2 = 2380 (the remainder is 0, so 2 is a divisor of 4760)
4760 / 3 = 1586.6666666667 (the remainder is 2, so 3 is not a divisor of 4760)
...
4760 / 4759 = 1.0002101281782 (the remainder is 1, so 4759 is not a divisor of 4760)
4760 / 4760 = 1 (the remainder is 0, so 4760 is a divisor of 4760)

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 4760 (i.e. 68.992753242641). 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 $\frac{N}{d} = D$ )

4760 / 1 = 4760 (the remainder is 0, so 1 and 4760 are divisors of 4760)
4760 / 2 = 2380 (the remainder is 0, so 2 and 2380 are divisors of 4760)
4760 / 3 = 1586.6666666667 (the remainder is 2, so 3 is not a divisor of 4760)
...
4760 / 67 = 71.044776119403 (the remainder is 3, so 67 is not a divisor of 4760)
4760 / 68 = 70 (the remainder is 0, so 68 and 70 are divisors of 4760)