Question

Сколько различных натуральных чисел от 4 до 1004 включительно, не делящихся ни на 5, ни на 8?

Answer 1

1004 - 4 + 1 =1001

Пусть Х - числа, делящ. на 5

Пусть У  -  числа, делящ. на 8

Х=1004/5 = 200

У=1004/8 = 125

Х ∩ У = 1004/40 =25

200 чисел  делятся на 5;

125 делятся  делятся на 8;

25 - делятся и на 5, и на 8 (то есть делятся на 40);

200+125-25=300

1001 -300=701 не делящихся ни на 5, ни на 8

Ответ: 701

Answer 2

Number of Natural Numbers from 4 to 1004 (inclusive) that are not divisible by 5 or 8

To find the number of natural numbers from 4 to 1004 (inclusive) that are not divisible by 5 or 8, we need to subtract the count of numbers divisible by 5 or 8 from the total count of numbers in that range.

The count of numbers divisible by 5 can be calculated by finding the number of multiples of 5 in that range. Similarly, the count of numbers divisible by 8 can be calculated by finding the number of multiples of 8 in that range.

Let's calculate the count of numbers divisible by 5 and 8 in the given range:

- Count of numbers divisible by 5: The first multiple of 5 in the given range is 5, and the last multiple of 5 is 1000. We can calculate the count of multiples of 5 using the formula: (last_multiple - first_multiple) / divisor + 1. In this case, the count of numbers divisible by 5 is (1000 - 5) / 5 + 1 = 200.

- Count of numbers divisible by 8: The first multiple of 8 in the given range is 8, and the last multiple of 8 is 1000. We can calculate the count of multiples of 8 using the same formula: (last_multiple - first_multiple) / divisor + 1. In this case, the count of numbers divisible by 8 is (1000 - 8) / 8 + 1 = 125.

Now, let's subtract the count of numbers divisible by 5 or 8 from the total count of numbers in the given range:

- Total count of numbers in the range from 4 to 1004 (inclusive): 1004 - 4 + 1 = 1001.

- Count of numbers divisible by 5 or 8: We need to find the count of numbers divisible by both 5 and 8, and subtract it from the sum of counts of numbers divisible by 5 and 8.

To find the count of numbers divisible by both 5 and 8, we need to find the count of multiples of the least common multiple (LCM) of 5 and 8, which is 40. The first multiple of 40 in the given range is 40, and the last multiple of 40 is 1000. We can calculate the count of multiples of 40 using the same formula: (last_multiple - first_multiple) / divisor + 1. In this case, the count of numbers divisible by both 5 and 8 is (1000 - 40) / 40 + 1 = 24.

Therefore, the count of numbers divisible by 5 or 8 is 200 + 125 - 24 = 301.

Finally, we can calculate the count of numbers from 4 to 1004 (inclusive) that are not divisible by 5 or 8 by subtracting the count of numbers divisible by 5 or 8 from the total count of numbers in the given range:

1001 - 301 = 700.

Therefore, there are 700 different natural numbers from 4 to 1004 (inclusive) that are not divisible by 5 or 8.