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WHAT is relatively prime

Math lesson

Mutually prime numbers - a mathematical concept, which should not be confused with simple numbers.

The total is only between the two concepts is that both of them are directly related to the division.

Simple mathematics called number suchthat can only be divided by one and by itself. 3, 7, 11, 143 or even 1,111,111 - all prime numbers, each of which has this property individually.
To speak of the relatively prime numbers, there should be at least two. This concept describes the common symptom of several numbers.

Definition of mutually prime numbers

These are called coprime numbers that do not have a common factor, not including units - for example, 3 and 5. In this case, each number separately can not be simple by itself.
For example, the number of 8 does not apply to those, becauseit can be divided by 2 and 4, 8 and 11, but - coprime numbers. The defining feature here is the absence of a common factor, rather than the characteristics of the individual numbers.
However, two or more prime numbers will always be relatively prime. If each of them is divisible only by one and itself, the common factor they can not be.
For relatively prime numbers there is a specialdesignation of a horizontal line and dropped it perpendicular. This is consistent with the property of perpendicular lines that do not have a common direction, as these include no common divisor.

Pairwise relatively prime numbers

It is possible for a combination of relatively prime numbers,from which you can take any two numbers at random, and they will prove to be relatively prime. For example, 2, 3 and 5: the total lack of any divider 2 and 3 or 2 and 5 or 5 and 3. These numbers refer pairwise relatively prime.
Not always are relatively prime in pairsrelatively prime. For example, the numbers 15, 20 and 21 - is relatively prime, but pairwise relatively prime can not name them, because 15 and 20 are divided into 5, and 15 and 21 - 3.

The use of relatively prime numbers

The chain transmission is usually the amount ofchain links and sprocket teeth are expressed relatively prime. Because of this, each of the teeth in contact with each link of the chain in turn, less wear mechanism.
There is even more interesting propertyrelatively prime numbers. It is necessary to draw a rectangle, the length and width of which are expressed in relatively prime, and spend out of the corner of a rectangle inside the beam angle of 45 degrees. At the point of contact with the side of the rectangle of the beam need to draw another beam, located at 90 degrees to the first - reflection. By making these rays, reflection time and time again, you can get the geometrical pattern in which any part of the structure is similar to the whole. In mathematical terms, the pattern is a fractal.

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