# Divisors Calculator

**Divisors of the number 40: **1, 2, 4, 5, 8, 10, 20, 40

**Number of divisors: **8

**The sum of its divisors: **90

Input a positive integer and this calculator will calculate:

• the complete list of divisors of the given number

• the sum of its divisors,

• the number of divisors

## What is a divisor

If we have a natural number p, then the number q is a divisor of the number p if it is true that it divides it without a remainder. So there is a natural number k such that k*q=p. The number p is also called the divisor, q is the divisor, and k is the quotient. Every natural number has at least two divisors. The number 1 (one) and itself, because 1*p=p*1=p. They are called trivial divisors. The number 0 (zero) is not a natural number but has infinitely many divisors - all numbers except zero.
The set of divisors can be calculated for all natural numbers. The usual procedure is to prime factorization the number p and obtain the divisors as a product of permutations of the prime factors. The list of divisors can also be obtained for small numbers by dividing the number p by numbers from 1 to the square root of p. Divisors have many uses in mathematics.