Question

Сколько существует натуральных чисел, не превосходящих 20210 не делящихся ни на 17, ни на 113

Answer 1

Ответ:

17145

Пошаговое объяснение:

20210 : 113=178 и 106 в остатке

20210:7=2887 и 1 в остатке. 103 на 7 не делится,

значит число чисел кратных 17 или 113 равно 2887+178=3065,

а  искомое число  20210-3065=17 145

Answer 2

Number of Natural Numbers Not Exceeding 20210 and Not Divisible by 17 or 113

To find the number of natural numbers not exceeding 20210 that are not divisible by 17 or 113, we can use the principle of inclusion-exclusion.

First, we find the number of natural numbers not exceeding 20210 that are divisible by 17 and 113, and then subtract this from the total count of natural numbers not exceeding 20210.

Step 1: Find the Count of Numbers Divisible by 17 and 113

The count of numbers divisible by 17 and 113 can be calculated using the formula for finding the count of multiples of a number within a range. The formula is:

\[ \left\lfloor\frac{n}{m}\right\rfloor \]

Where: - \(\left\lfloor x \right\rfloor\) represents the greatest integer less than or equal to x. - n is the upper limit (20210 in this case). - m is the product of 17 and 113.

Using this formula, we can calculate the count of numbers divisible by 17 and 113.

Step 2: Find the Total Count of Natural Numbers Not Exceeding 20210

The total count of natural numbers not exceeding 20210 is simply 20210.

Step 3: Apply the Principle of Inclusion-Exclusion

We then subtract the count of numbers divisible by 17 and 113 from the total count of natural numbers not exceeding 20210 to find the number of natural numbers not exceeding 20210 that are not divisible by 17 or 113.

Let's calculate these values using the provided search results.