Question

Число a - натуральное число меньше 45, которое не делится на 2, на 3 и на 5. Верно ли, что a - простое число? Ответ объясните.

Answer 1

Пусть такое число n, n не может делиться на 4 и на 6 (иначе бы оно делилось на 2), следующий вариант для n - 7, (8, 9, 10) - неподходят, 11 - простое, подходит. Далее (12) - делится на 2, 13 - простое подходит. 14,15,16 - неподходят, 17 - простое подходит. 18 - делиться на 2, 19 - простое подходит, (20,21,22) - мимо, 23 - простое подходит. Далее перебираешь вот таким вот методом. Называется оно метод числового решета (в вики есть даже красивая анимация :))

Answer 2

Число а = 7  11  13  17  19  23  29  31  37 43-это   простые числа,  потому что делятся на 1 и само себя,а   на другие числа не делятся.

Answer 3

Is a a Prime Number?

To determine whether a is a prime number, we need to check if it is divisible by any number other than 1 and itself. In this case, a is a natural number less than 45 that is not divisible by 2, 3, and 5.

Let's analyze the possible values of a and determine if they are prime numbers.

- If a is 1, it is not a prime number because prime numbers are defined as natural numbers greater than 1 that have no positive divisors other than 1 and itself.

- If a is 2, it is a prime number because it is only divisible by 1 and 2.

- If a is 3, it is a prime number because it is only divisible by 1 and 3.

- If a is 4, it is not a prime number because it is divisible by 2.

- If a is 5, it is a prime number because it is only divisible by 1 and 5.

- If a is 6, it is not a prime number because it is divisible by 2 and 3.

- If a is 7, it is a prime number because it is only divisible by 1 and 7.

- If a is 8, it is not a prime number because it is divisible by 2.

- If a is 9, it is not a prime number because it is divisible by 3.

- If a is 10, it is not a prime number because it is divisible by 2 and 5.

Based on this analysis, we can see that not all values of a are prime numbers. For example, a = 4, 6, 8, and 10 are not prime numbers because they are divisible by numbers other than 1 and themselves.

Therefore, it is not correct to say that a is always a prime number. The statement "a is a prime number" is false for some values of a.