What are the divisors of 1201?

1, 1201

There is a total of 2 positive divisors.
The sum of these divisors is 1202.
The arithmetic mean is 601.

2 odd divisors

1, 1201

How to compute the divisors of 1201?

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 1201 by each of the numbers from 1 to 1201 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)

1201 / 1 = 1201 (the remainder is 0, so 1 is a divisor of 1201)
1201 / 2 = 600.5 (the remainder is 1, so 2 is not a divisor of 1201)
1201 / 3 = 400.33333333333 (the remainder is 1, so 3 is not a divisor of 1201)
...
1201 / 1200 = 1.0008333333333 (the remainder is 1, so 1200 is not a divisor of 1201)
1201 / 1201 = 1 (the remainder is 0, so 1201 is a divisor of 1201)

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 1201 (i.e. 34.655446902327). 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 $\frac{N}{d} = D$ )

1201 / 1 = 1201 (the remainder is 0, so 1 and 1201 are divisors of 1201)
1201 / 2 = 600.5 (the remainder is 1, so 2 is not a divisor of 1201)
1201 / 3 = 400.33333333333 (the remainder is 1, so 3 is not a divisor of 1201)
...
1201 / 33 = 36.393939393939 (the remainder is 13, so 33 is not a divisor of 1201)
1201 / 34 = 35.323529411765 (the remainder is 11, so 34 is not a divisor of 1201)