What are the divisors of 4702?

1, 2, 2351, 4702

There is a total of 4 positive divisors.
The sum of these divisors is 7056.
The arithmetic mean is 1764.

2 even divisors

2, 4702

2 odd divisors

1, 2351

How to compute the divisors of 4702?

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 4702 by each of the numbers from 1 to 4702 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)

4702 / 1 = 4702 (the remainder is 0, so 1 is a divisor of 4702)
4702 / 2 = 2351 (the remainder is 0, so 2 is a divisor of 4702)
4702 / 3 = 1567.3333333333 (the remainder is 1, so 3 is not a divisor of 4702)
...
4702 / 4701 = 1.0002127206977 (the remainder is 1, so 4701 is not a divisor of 4702)
4702 / 4702 = 1 (the remainder is 0, so 4702 is a divisor of 4702)

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 4702 (i.e. 68.571130951735). 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 $\frac{N}{d} = D$ )

4702 / 1 = 4702 (the remainder is 0, so 1 and 4702 are divisors of 4702)
4702 / 2 = 2351 (the remainder is 0, so 2 and 2351 are divisors of 4702)
4702 / 3 = 1567.3333333333 (the remainder is 1, so 3 is not a divisor of 4702)
...
4702 / 67 = 70.179104477612 (the remainder is 12, so 67 is not a divisor of 4702)
4702 / 68 = 69.147058823529 (the remainder is 10, so 68 is not a divisor of 4702)