In the most general case, the quantity of possible dividers of any number is infinite. Actually, all this numbers not equal to zero. But if it is about natural numbers, then the divider of number N is meant as such natural number into which number N totally is divided. The quantity of such dividers is always limited, and it is possible to find them by means of special algorithms. Also there are simple dividers of number which represent prime numbers.
It is required to you
- - table of prime numbers;
- - criteria for divisibility of numbers;
- - calculator.
Instruction
1. Most often, it is necessary to spread out number to simple multipliers. It numbers which divide initial number without the rest and at the same time can be divided without the rest only into themselves and unit (treat such numbers 2, 3, 5, 7, 11, 13, 17, etc.). And, no regularity among prime numbers is found. Take them from the special table or find by means of an algorithm which is called "Eratosthenes's sieve".
2. Begin to select prime numbers into which this number is divided. Private you divide into a prime number again and you continue this process until as private there is no prime number. Then just count quantity of simple dividers, add to it number 1 (which considers the last private). The quantity of simple dividers which at multiplication will give required number will be result.
3. For example, find quantity of simple dividers of number 364 thus: 364/2=182182/2=9191/7=13poluchite number 2, 2, 7, 13 which are simple natural dividers of number 364. Their quantity is equal 3 (if to consider the repeating dividers for one).
4. If it is necessary to find total number of all possible natural dividers of number, use its initial decomposition. For this purpose by the technique described above spread out number to simple multipliers. Then write down number as the work of such multipliers. Build the repeating numbers in degree, for example, if received a divider 5 three times, then write down it as 5³.
5. Write down the work from the smallest multipliers to the greatest. Such work is also called initial decomposition of number. Each multiplier of this decomposition has the degree presented by natural number (1, 2, 3, 4, etc.). Designate exponents at multipliers a1, a2, a3, etc. Then the total number of dividers will be equal to the work (a1 + 1) ∙ (a2 + 1) ∙ (a3+1) ∙ …
6. For example, take the same number 364: its initial decomposition 364=2² ∙ 7∙13. Receive a1=2, a2=1, a3=1, then the quantity of natural dividers of this number will be equal (2+1) ∙ (1+1) ∙ (1+1) =3∙2∙2=12.