What are the divisors of 701?

1, 701

There is a total of 2 positive divisors.
The sum of these divisors is 702.
The arithmetic mean is 351.

2 odd divisors

1, 701

How to compute the divisors of 701?

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 701 by each of the numbers from 1 to 701 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)

701 / 1 = 701 (the remainder is 0, so 1 is a divisor of 701)
701 / 2 = 350.5 (the remainder is 1, so 2 is not a divisor of 701)
701 / 3 = 233.66666666667 (the remainder is 2, so 3 is not a divisor of 701)
...
701 / 700 = 1.0014285714286 (the remainder is 1, so 700 is not a divisor of 701)
701 / 701 = 1 (the remainder is 0, so 701 is a divisor of 701)

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 701 (i.e. 26.476404589747). 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 $\frac{N}{d} = D$ )

701 / 1 = 701 (the remainder is 0, so 1 and 701 are divisors of 701)
701 / 2 = 350.5 (the remainder is 1, so 2 is not a divisor of 701)
701 / 3 = 233.66666666667 (the remainder is 2, so 3 is not a divisor of 701)
...
701 / 25 = 28.04 (the remainder is 1, so 25 is not a divisor of 701)
701 / 26 = 26.961538461538 (the remainder is 25, so 26 is not a divisor of 701)