What are the divisors of 1262?

1, 2, 631, 1262

There is a total of 4 positive divisors.
The sum of these divisors is 1896.
The arithmetic mean is 474.

2 even divisors

2, 1262

2 odd divisors

1, 631

How to compute the divisors of 1262?

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 1262 by each of the numbers from 1 to 1262 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)

1262 / 1 = 1262 (the remainder is 0, so 1 is a divisor of 1262)
1262 / 2 = 631 (the remainder is 0, so 2 is a divisor of 1262)
1262 / 3 = 420.66666666667 (the remainder is 2, so 3 is not a divisor of 1262)
...
1262 / 1261 = 1.0007930214116 (the remainder is 1, so 1261 is not a divisor of 1262)
1262 / 1262 = 1 (the remainder is 0, so 1262 is a divisor of 1262)

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 1262 (i.e. 35.524639336663). 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 $\frac{N}{d} = D$ )

1262 / 1 = 1262 (the remainder is 0, so 1 and 1262 are divisors of 1262)
1262 / 2 = 631 (the remainder is 0, so 2 and 631 are divisors of 1262)
1262 / 3 = 420.66666666667 (the remainder is 2, so 3 is not a divisor of 1262)
...
1262 / 34 = 37.117647058824 (the remainder is 4, so 34 is not a divisor of 1262)
1262 / 35 = 36.057142857143 (the remainder is 2, so 35 is not a divisor of 1262)