Question

Сколько трёхзначных чисел имеют нечётное количество натуральных делителей?

Answer 1

Ответ:

вот примерно таким тип должен быть ответ

Answer 2

Number of Three-Digit Numbers with an Odd Number of Natural Divisors

To determine the number of three-digit numbers that have an odd number of natural divisors, we need to consider the properties of perfect squares.

A perfect square is a number that can be expressed as the square of an integer. For example, 9 is a perfect square because it can be expressed as 3^2.

The number of divisors of a perfect square is always odd. This is because each divisor has a corresponding divisor that, when multiplied together, equals the perfect square. For example, the divisors of 9 are 1, 3, and 9. The pairs of divisors are (1, 9) and (3, 3), which multiply to give 9.

In the case of three-digit numbers, we need to find the perfect squares that fall within the range of three-digit numbers. The perfect squares between 100 and 999 are 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, and 900.

Therefore, there are 20 three-digit numbers that have an odd number of natural divisors.