What are the divisors of 901?

1, 17, 53, 901

There is a total of 4 positive divisors.
The sum of these divisors is 972.
The arithmetic mean is 243.

4 odd divisors

1, 17, 53, 901

How to compute the divisors of 901?

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 901 by each of the numbers from 1 to 901 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)

901 / 1 = 901 (the remainder is 0, so 1 is a divisor of 901)
901 / 2 = 450.5 (the remainder is 1, so 2 is not a divisor of 901)
901 / 3 = 300.33333333333 (the remainder is 1, so 3 is not a divisor of 901)
...
901 / 900 = 1.0011111111111 (the remainder is 1, so 900 is not a divisor of 901)
901 / 901 = 1 (the remainder is 0, so 901 is a divisor of 901)

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 901 (i.e. 30.016662039607). 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 $\frac{N}{d} = D$ )

901 / 1 = 901 (the remainder is 0, so 1 and 901 are divisors of 901)
901 / 2 = 450.5 (the remainder is 1, so 2 is not a divisor of 901)
901 / 3 = 300.33333333333 (the remainder is 1, so 3 is not a divisor of 901)
...
901 / 29 = 31.068965517241 (the remainder is 2, so 29 is not a divisor of 901)
901 / 30 = 30.033333333333 (the remainder is 1, so 30 is not a divisor of 901)