Identify the Number: Divisibility Challenge with 10, 4, and 2

To solve this problem, we'll analyze each choice using divisibility rules for 10, 4, and 2:

• Divisibility by 10: The number must end in 0.

• Divisibility by 4: The last two digits of the number must form a number divisible by 4.

• Divisibility by 2: The number must end in an even digit, specifically 0, 2, 4, 6, or 8.

Now, let's evaluate each choice:

• 45:
  Ending digit is 5. Not divisible by 10 or 2, so it cannot be divisible by all three.

• 30:
  Ending digit is 0 (divisible by 10 and 2).
  Last two digits form 30, which is not divisible by 4 (30/4 = 7.5). So, it cannot be divisible by all three.

• 35:
  Ending digit is 5. Not divisible by 10 or 2, so it cannot be divisible by all three.

• 40:
  Ending digit is 0 (divisible by 10 and 2).
  Last two digits form 40, which is divisible by 4 (40/4 = 10).
  Therefore, 40 is divisible by 10, 4, and 2.

Therefore, the number that is divisible by 10, 4, and 2 is $40$.