What are the divisors of 62?

1, 2, 31, 62

There is a total of 4 positive divisors.
The sum of these divisors is 96.
The arithmetic mean is 24.

2 even divisors

2, 62

2 odd divisors

1, 31

How to compute the divisors of 62?

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 62 by each of the numbers from 1 to 62 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)

62 / 1 = 62 (the remainder is 0, so 1 is a divisor of 62)
62 / 2 = 31 (the remainder is 0, so 2 is a divisor of 62)
62 / 3 = 20.666666666667 (the remainder is 2, so 3 is not a divisor of 62)
...
62 / 61 = 1.016393442623 (the remainder is 1, so 61 is not a divisor of 62)
62 / 62 = 1 (the remainder is 0, so 62 is a divisor of 62)

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 62 (i.e. 7.8740078740118). 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 $\frac{N}{d} = D$ )

62 / 1 = 62 (the remainder is 0, so 1 and 62 are divisors of 62)
62 / 2 = 31 (the remainder is 0, so 2 and 31 are divisors of 62)
62 / 3 = 20.666666666667 (the remainder is 2, so 3 is not a divisor of 62)
...
62 / 6 = 10.333333333333 (the remainder is 2, so 6 is not a divisor of 62)
62 / 7 = 8.8571428571429 (the remainder is 6, so 7 is not a divisor of 62)