What are the divisors of 151?

1, 151

There is a total of 2 positive divisors.
The sum of these divisors is 152.
The arithmetic mean is 76.

2 odd divisors

1, 151

How to compute the divisors of 151?

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 151 by each of the numbers from 1 to 151 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)

151 / 1 = 151 (the remainder is 0, so 1 is a divisor of 151)
151 / 2 = 75.5 (the remainder is 1, so 2 is not a divisor of 151)
151 / 3 = 50.333333333333 (the remainder is 1, so 3 is not a divisor of 151)
...
151 / 150 = 1.0066666666667 (the remainder is 1, so 150 is not a divisor of 151)
151 / 151 = 1 (the remainder is 0, so 151 is a divisor of 151)

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 151 (i.e. 12.288205727445). 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 $\frac{N}{d} = D$ )

151 / 1 = 151 (the remainder is 0, so 1 and 151 are divisors of 151)
151 / 2 = 75.5 (the remainder is 1, so 2 is not a divisor of 151)
151 / 3 = 50.333333333333 (the remainder is 1, so 3 is not a divisor of 151)
...
151 / 11 = 13.727272727273 (the remainder is 8, so 11 is not a divisor of 151)
151 / 12 = 12.583333333333 (the remainder is 7, so 12 is not a divisor of 151)