# Divisors

A number is a divisor of another when it divides exactly.

4 is a divisor of 12; 12 : 4 = 3.

The divisors are also called** factors**.

### Properties of the Divisors

1. A number, other than 0, is a divisor of itself.

2. The number **1** is a divisor of all numbers.

3.Any divisor of a number other than zero is smaller than or equal to it, therefore the number of divisors are finite.

4. If a number is a divisor of two others, it is also a divisor of their sum and their difference.

5. If a number is a divisor of another, it is also a divisor of all the multiples of that number.

6. If a number is a divisor of another number, and that number is a divisor of a third one, the first number is also a divisor of the third number.

### Prime Factorization

To decompose a number into factors, make successive divisions among its prime divisors to obtain one as the quotient.

To make the divisions use a vertical bar, to the right write the prime divisors and to the left the quotients.

2,520 = 2^{3 } · 3^{2 } · 5 · 7

### Number of Divisors

It is obtained by adding the unit to the exponents and multiplying the obtained results:

Number of dividers of 2,520 = (3+1) · (2+1) · (1 + 1) · (1 + 1) = 48