To factorize number, it is necessary to specify whether the number is composite as process of decomposition is a division of a composite number into prime numbers. The prime number is divided only into 1 and into itself. And unit is not either a simple, nor composite number. For simplification of process and obtaining fast result it is necessary to know signs of division of numbers on 2, on 3, on 5, on 10, etc.
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1. If number small, then itdecompositionjust to make on the basis of the multiplication table. For example, it is required to factorize number 6. It is known that 6 = 2 x 3. Numbers 2 and 3 prime, respectively, these numbers are also simple multipliers of number 6. At decomposition of number 49 we receive 7 and 7 as 49 = 7 x 7.
2. At a large number at first it is necessary to divide it into the smallest prime number which is its divider. And so on, before obtaining full result. For example, it is required to spread out number 242 to simple multipliers. The smallest divider of this number - number 2. We receive: 242: 2 = 121. Further we look for the smallest divider of number 121. It is obvious what neither on 2, nor on 3, nor on 5, nor is not divided into the 7th this number. Thus, we touch prime numbers on their increase. Number 121 is divided into 11. We receive: 121: 11 = 11. Number 11, naturally, is divided only into 11. So, 11: 11 = 1. As a result we receive that simple multipliers of composite number 242 are numbers: 2, 11 and 11. It can be written down in the form of the work: 242 = 2 x 11 x 11 or 242 = 2 x 11 ^ 2.
3. For simplification of a problem of decomposition it is possible to use the table of prime numbers. According to the table we look for the smallest divider in the way of search. We divide into it this number and further, the same way we look for the smallest divider of the received number. We make such actions until as a result we do not receive a prime number. For example, it is necessary to spread out number 1454 to simple multipliers. We look in the table. On the first place number 2. It suits us: 1738: 2 = 869. Further according to the table we look for number into which 869 is divided. Using criteria for divisibility of numbers, becomes obvious that it is 11. 869: 11 = 79. And number 79 is simple, it is visible from the table. From this it follows that simple multipliers of number 1738 are 2, 11 and 79. The result can be written down in a look: 1738 = 2 x 11 x 79.