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.
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 = 2³ · 3² · 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