If the number 42573* is exactly divisible by 12, then which of the following number should replace *? Options4576

The number 12 is divisible by both 3 and 4. Therefore, for a number to be divisible by 12, it must be divisible by both 3 and 4.

1. For a number to be divisible by 3, the sum of its digits must be divisible by 3. In the number 42573*, the sum of the digits 4+2+5+7+3 = 21. Since 21 is divisible by 3, the number is divisible by 3 regardless of what digit replaces the *.

2. For a number to be divisible by 4, the last two digits must form a number that is divisible by 4. In the number 42573*, the last two digits are 3 and . Therefore, the number formed by 3 must be divisible by 4.

The options given are 4, 5, 7, and 6.

• If * is replaced by 4, the last two digits form the number 34, which is not divisible by 4.
• If * is replaced by 5, the last two digits form the number 35, which is not divisible by 4.
• If * is replaced by 7, the last two digits form the number 37, which is not divisible by 4.
• If * is replaced by 6, the last two digits form the number 36, which is divisible by 4.

Therefore, the number that should replace * to make 42573* divisible by 12 is 6.