Question

Доказать, что любое трёхзначное число, записано одинаковыми цыфрами, делится на 37.

Answer 1

Ааа-трехзначное число, можно записать в виде а·111, число 111 делится на 37 (111:37=3), значит и число ааа делится на 37

Answer 2

Proof that Any Three-Digit Number with Identical Digits is Divisible by 37

To prove that any three-digit number with identical digits is divisible by 37, we can use the fact that 1/37 is a repeating decimal with a cycle of 3 digits. This means that any number formed by repeating the same digit three times will be divisible by 37. Let's demonstrate this:

Step 1: Consider the three-digit number formed by repeating the digit 'a' three times, i.e., aaa.

Step 2: Express aaa as a mathematical expression: aaa = 111a.

Step 3: Now, we can express 111 as 37 * 3, showing that 111 is divisible by 37.

Step 4: Therefore, aaa = 111a is also divisible by 37.

This demonstrates that any three-digit number with identical digits is divisible by 37.