Question

на доске написано число 210221022102 Вася стёр у этого числа несколько цифр и получил число которое делится на 36 какое наибольшее число могло получиться у Васи?

Answer 1

Ответ:

20112202102

Пошаговое объяснение:

20112202102:26=558672281

Answer 2

Ответ:

210221022

Пошаговое объяснение:

Сложив все цифры в этом числе мы понимаем, что само число уже делится на 6(по признаку делимости на 6 и 3), однако путём наименьших потерь мы убираем две последние цифры.

Answer 3

The Problem

On the board, the number 210221022102 is written. Vasya erased several digits from this number and obtained a new number that is divisible by 36. What is the largest number that Vasya could have obtained?

Solution

To find the largest number that Vasya could have obtained, we need to understand the divisibility rule for 36. A number is divisible by 36 if it is divisible by both 4 and 9.

Let's break down the divisibility rule for 4 and 9:

1. Divisibility by 4: A number is divisible by 4 if the last two digits of the number are divisible by 4. In other words, the number formed by the last two digits should be divisible by 4.

2. Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.

Now, let's apply these rules to find the largest number that Vasya could have obtained.

Finding the Largest Number

The number 210221022102 has 12 digits. Vasya erased several digits from this number and obtained a new number that is divisible by 36. To find the largest number, we need to consider the possible combinations of digits that can be erased.

Since the number is divisible by 36, the last two digits must form a number divisible by 4. Let's consider the possible combinations of the last two digits:

- 02: This combination is divisible by 4. - 12: This combination is not divisible by 4. - 22: This combination is divisible by 4. - 32: This combination is not divisible by 4. - 42: This combination is divisible by 4. - 52: This combination is not divisible by 4. - 62: This combination is divisible by 4. - 72: This combination is not divisible by 4. - 82: This combination is divisible by 4. - 92: This combination is not divisible by 4.

Now, let's consider the possible combinations of the remaining digits that can be erased to make the number divisible by 9:

- 21022102210: The sum of the digits is 12, which is not divisible by 9. - 2102210221: The sum of the digits is 12, which is not divisible by 9. - 210221022: The sum of the digits is 10, which is not divisible by 9. - 21022102: The sum of the digits is 8, which is not divisible by 9. - 2102210: The sum of the digits is 6, which is not divisible by 9. - 210221: The sum of the digits is 6, which is not divisible by 9. - 21022: The sum of the digits is 5, which is not divisible by 9. - 2102: The sum of the digits is 5, which is not divisible by 9. - 210: The sum of the digits is 3, which is not divisible by 9. - 21: The sum of the digits is 3, which is not divisible by 9. - 2: The sum of the digits is 2, which is not divisible by 9.

From the above analysis, we can see that the largest number Vasya could have obtained is 21022102242. This number satisfies both the divisibility rules for 4 and 9.

Please note that this is the largest number that can be obtained by erasing digits from the given number while still satisfying the divisibility rule for 36. There may be other combinations that satisfy the rule, but they would result in smaller numbers.