- - a table of Prime numbers;
- - divisibility rules of numbers;
- calculator.

364/2=182

182/2=91

91/7=13

Get numbers 2, 2, 7, 13, which are simple natural divisors of the number 364. Their number is equal to 3 (if you count the duplicate splitters in one).

# Advice 2: How to find all factors of a number

**number**a, if there is an integer q such that bq = a. Usually considered the divisibility of natural numbers. The dividend itself will be called a multiple of

**the number**b. Search all divisors

**of the number**is carried out according to certain rules.

- Divisibility rules

**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.

**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**.

**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.

**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**.

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

# Advice 3: How to find least common multiple of numbers

## Finding least common multiple: basic concepts

To understand how to calculate LCM, should be determined primarily by the value of the term "multiples".

A multiple of the number And call this natural number which evenly divides into A. So, multiples of 5 can be considered 15, 20, 25 and so on.

Of divisors of a particular number can be limited, but a multiple of an infinite set.

Common multiple of natural numbers is a number that divides them without a remainder.

## How to find least common multiple of numbers

Least common multiple (LCM) of numbers (two, three or more) is the smallest natural number that is divisible by all those numbers evenly.

To find the LCM, you can use several ways.

For small numbers it is convenient to write in the line are all multiples of these numbers until for are common. Multiples indicate in the record the capital letter K.

For example, a multiple of the number 4 can be written as:

To (4) = {8,12, 16, 20, 24, ...}

To (6) = {12, 18, 24, ...}

So, you can see that the least common multiple of numbers 4 and 6 is the number 24. This recording is performed as follows:

Knock (4, 6) = 24

If the numbers are large, or need to find the least common multiple of three or more numbers, it is better to use a different method to calculate the NOC.

To perform the job must be expanded the proposed number into Prime factors.

First you need to write in place of the decomposition of most of the numbers and the rest.

In the decomposition of each number may contain a different number of multipliers.

For example, decompose into Prime factors of the number 50 and 20.

50 = 2 * 5 * 5

20 = 2 * 5 * 2

In the decomposition of a smaller number, it should be emphasized multipliers, which are absent in the decomposition of the first of a very large number and then add to it. In the presented example is not enough of two.

You can now calculate the least common multiple of 20 and 50.

NOC (20, 50) = 2 * 5 * 5 * 2 = 100

So, the product of the Prime factors of a larger number of factors of the second numbers, which are not included in the expansion of the greater will be the lowest common multiple.

To find the NOC three numbers or more, they should all be decomposed into Prime factors, as in the previous case.

As an example, it is possible to find the least common multiple of the numbers 16, 24, 36.

36 = 2 * 2 * 3 * 3

24 = 2 * 2 * 2 * 3

16 = 2 * 2 * 2 * 2

So, in the expansion of the greater number of the multipliers does not include only two twos from the decomposition of sixteen (one is in the decay of twenty-four).

Thus, you need to add them to the decomposition of the greater number.

NOC (12, 16, 36) = 2 * 2 * 3 * 3 * 2 * 2 = 9

There are special cases of determining the least common multiple. So, if one of the numbers can be evenly divided by another, the larger of these numbers will be the least common multiple.

For example, the NOC of twelve and twenty-four is twenty-four.

If you want to find the least common multiple of relatively Prime numbers that do not have the same divisors, their NOC will be equal to their product.

For example, LCM (10, 11) = 110.

# Advice 4: How to find least common divisor

**divisor**of the denominators and calculate.

- - the ability to decompose the number into Prime factors;
- - the ability to perform operations with fractions.