Divisibility by 4: Complete the Number 213_2

Question

Complete the number so that it is divisible by 4 without a remainder:

213 — 2 213\text{ }_{—\text{ }}2

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the rule for divisibility by 4.

  • Step 2: Apply this rule to the number — 2 _{—\text{ }}2 .

  • Step 3: Test each possible digit for the missing number to find a two-digit number divisible by 4.

Now, let's work through each step:
Step 1: The divisibility rule for 4 is that a number is divisible by 4 if the last two digits form a number divisible by 4.
Step 2: In the number 213 — 2213\text{ }_{—\text{ }}2, the last two digits are _{\—\text{ }}2. We want this two-digit number to be divisible by 4.
Step 3: Test the potential digits for blank using the choices given:

  • If the blank is 0, the last two digits are 02, which is divisible by 4. But this isn't provided as a solution in the context.

  • If the blank is 2, the last two digits are 22, which is not divisible by 4.

  • If the blank is 3, the last two digits are 32, which is divisible by 4.

  • If the blank is 4, the last two digits are 42, which is not divisible by 4.

Checking through these options shows that placing a 3 in the blank makes the number divisible by 4.

Therefore, the solution to the problem is 3 3 .

Answer

3