Complete 21__ to Make it Divisible by 4

Q: Why do I only need to check the last two digits?

The divisibility rule for 4 states that if the last two digits of any number are divisible by 4, then the entire number is divisible by 4. This works because 100, 1000, 10000... are all divisible by 4!

Q: What if I get multiple correct answers?

That's possible! For this problem, we need to find which two-digit combination from the given choices makes the number divisible by 4. Check each option systematically.

Q: How do I quickly check if a two-digit number divides by 4?

For numbers ending in even digits: 12, 16, 20, 24, 28, 32, 36, 40, 44, 48... are divisible by 4. You can memorize these patterns or do quick division.

Q: What's the difference between remainder 0 and no remainder?

These mean the same thing! When we say 'no remainder' or 'remainder 0', it means the division is exact with no leftover amount.

Q: Can I use a calculator to check my answer?

Yes! Divide your complete number by 4. If you get a whole number (like 531, not 531.25), then your answer is correct.

Divisibility Rules with Last Two Digits

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

$21\text{ }_{—\text{ —}}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the digits so that the number is divisible by 4

00:03 Multiply the tens digit by 2, and add to it the ones digit:

00:07 If this number is divisible by 4, then the number itself is divisible by 4

00:12 According to this method, we'll go through all the numbers and eliminate accordingly

00:49 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

$21\text{ }_{—\text{ —}}$

Step-by-step solution

To solve the problem, we will ensure the two-digit number formed from the missing blanks at the end of 21 is divisible by 4. This requires performing the following steps:

Step 1: Identify combinations for the blanks. Since this is a two-digit number, consider each combination within the range of numbers provided.
Step 2: Check divisibility. Once the numbers are identified, check if they are divisible by 4.
Step 3: Validate the correct number. The rule is that it must divide evenly with no remainder.

Numbers formed by potential combinations from the given choices are:
- $212$ , $214$

Now, let's check each of these numbers:

$212$ : Dividing 212 by 4 gives $212 \div 4 = 53$ . This is an integer, meaning 212 is divisible by 4.
$214$ : Dividing 214 by 4 gives $214 \div 4 = 53.5$ . This is not an integer, hence 214 is not divisible by 4.

After evaluation, the number $212$ is divisible by 4.

The numbers that fill the blanks and ensure divisibility by 4 are 2, 4.

Final Answer

2, 4

Key Points to Remember

Essential concepts to master this topic

Rule: A number is divisible by 4 if its last two digits are divisible by 4
Technique: Check $24 \div 4 = 6$ to verify 2124 works
Check: Divide the complete number by 4 to confirm no remainder ✓

Common Mistakes

Avoid these frequent errors

Checking if the entire number divides by 4 instead of using the rule
Don't divide the whole number 2124 ÷ 4 from the start = unnecessary long division! This wastes time and increases error chances. Always use the divisibility rule: only check if the last two digits are divisible by 4.

Practice Quiz

Test your knowledge with interactive questions

Is the number 10 divisible by 4?

FAQ

Everything you need to know about this question

Why do I only need to check the last two digits?

The divisibility rule for 4 states that if the last two digits of any number are divisible by 4, then the entire number is divisible by 4. This works because 100, 1000, 10000... are all divisible by 4!

What if I get multiple correct answers?

That's possible! For this problem, we need to find which two-digit combination from the given choices makes the number divisible by 4. Check each option systematically.

How do I quickly check if a two-digit number divides by 4?

For numbers ending in even digits: 12, 16, 20, 24, 28, 32, 36, 40, 44, 48... are divisible by 4. You can memorize these patterns or do quick division.

What's the difference between remainder 0 and no remainder?

These mean the same thing! When we say 'no remainder' or 'remainder 0', it means the division is exact with no leftover amount.

Can I use a calculator to check my answer?

Yes! Divide your complete number by 4. If you get a whole number (like 531, not 531.25), then your answer is correct.

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