You will need

- Divisibility rules

Instruction

1

First, make sure that any natural number greater than one, has at least two divisors - one and itself. Indeed, a:1 = a, a:a = 1. Numbers that have only two divisors, are called simple. The only divider unit is obviously the unit. That is, one is not a Prime number (and is not composite, as we will see later).

2

Numbers that have more than two divisors are called composite. What

Since even

**number**can be composite?Since even

**numbers**are divisible by 2 divisible, then all the even**numbers**except**the number**2, are composite. Indeed, when dividing 2:2 deuce divided within itself, ie it has only two divisor (1 and 2) and is a simple number.3

Will see if there are an even

**number of**even some**dividers**. Divide it first by 2. From the commutative operation of multiplication it is obvious that the resulting quotient will also be a divisor of the**number**. Then, if the resulting quotient is an integer, and divide again by 2 already it's private. Then the resulting new quotient y = (x:2):2 = x:4 will also be a divisor of the original**numbers**. Similarly, 4 is a divisor of the original**numbers**.4

Continuing this chain, we can generalize the rule: sequentially divide an even number first and then the resulting private for 2 to until a certain individual will not be equal to an odd number. In this case, all the resulting private are divisors of this

**number**. In addition, the divisors of this**number**will be**the number**2^k where k = 1...n, where n is the number of steps of the chain.Example: 24:2 = 12, 12:2 = 6, 6:2 = 3 - an odd number. Consequently, the 12, 6 and 3**factors****of the number**24. In the chain 3 steps, therefore, divisors**of the number**24 will also be**the number**2^1 = 2 (already known from the parity**of the number**24), 2^2 = 4 2^3 = 8. Thus,**the number of**1, 2, 3, 4, 6, 8, 12 and 24 are divisors**of the number**24.5

However, not all even numbers, this scheme can give all

There are divisibility rules for certain

Divisibility by 3: when the sum of the digits

Divisibility by 5: last digit when

Divisibility by 7: when the result of subtracting twice the last digit from this

Divisibility by 9 when the sum of digits

Divisibility by 11: when the sum of digits occupying odd places, or equal to the sum of digits occupying odd places, or differ from it by a number divisible by 11.

There are also divisibility rules for 13, 17, 19, 23 and other

**the divisors****of the number**. Consider, for example, the number 42. 42:2 = 21. However, as we know,**the numbers**3, 6 and 7 will also be divisors**of the number**42.There are divisibility rules for certain

**numbers**. Will discuss the most important of them:Divisibility by 3: when the sum of the digits

**of the number**is divisible by 3 without a remainder.Divisibility by 5: last digit when

**the number**is 5 or 0.Divisibility by 7: when the result of subtracting twice the last digit from this

**number**the last number is divided by 7.Divisibility by 9 when the sum of digits

**of number**divisible by 9 without a remainder.Divisibility by 11: when the sum of digits occupying odd places, or equal to the sum of digits occupying odd places, or differ from it by a number divisible by 11.

There are also divisibility rules for 13, 17, 19, 23 and other

**numbers**.6

As for even and for odd numbers you need to use signs division for a particular number. Dividing a number, you should determine

**the divisors of**the resulting private, etc. (the chain is the same chain of even numbers by dividing them by 2, described above).