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

Q: Why does a number divisible by 10 automatically work for 2?

Great observation! Since divisibility by 10 requires ending in 0, and 0 is even, any number divisible by 10 is automatically divisible by 2. This means you really only need to check divisibility by 10 and 4!

Q: How do I quickly check if a number is divisible by 4?

Look at the last two digits only! If those two digits form a number divisible by 4, then the whole number is divisible by 4. For example: in 240, just check if 40 ÷ 4 = 10 (yes!).

Q: Why isn't 30 the right answer?

30 is tricky! It ends in 0 (divisible by 10 and 2), but the last two digits are 30. Since $ 30 ÷ 4 = 7.5 $, it's not divisible by 4. Remember: all conditions must be met!

Divisibility Rules with Multiple Conditions

Which of the following numbers is divisible by 10, 4 and 2?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose a number divisible by 2, 4, and 10

00:04 Let's try to divide each number by each of the factors

00:10 We'll eliminate all numbers that aren't divisible by all factors

00:30 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

Which of the following numbers is divisible by 10, 4 and 2?

Step-by-step solution

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 $40$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Numbers must satisfy all three divisibility tests simultaneously
Technique: Check by 10 (ends in 0), then by 4 (40÷4=10)
Check: Verify all conditions: 40 ends in 0, divisible by 2 and 4 ✓

Common Mistakes

Avoid these frequent errors

Testing divisibility rules separately without combining all conditions
Don't check each rule individually and pick any number that passes one test = wrong answer! A number like 30 passes tests for 10 and 2 but fails for 4. Always ensure the number satisfies ALL three conditions simultaneously.

Practice Quiz

Test your knowledge with interactive questions

Is the number 43 divisible by 4?

FAQ

Everything you need to know about this question

Why does a number divisible by 10 automatically work for 2?

Great observation! Since divisibility by 10 requires ending in 0, and 0 is even, any number divisible by 10 is automatically divisible by 2. This means you really only need to check divisibility by 10 and 4!

How do I quickly check if a number is divisible by 4?

Look at the last two digits only! If those two digits form a number divisible by 4, then the whole number is divisible by 4. For example: in 240, just check if 40 ÷ 4 = 10 (yes!).

What if none of the choices work?

Double-check your work! Make sure you're applying all three rules correctly. Remember: must end in 0 (for 10), last two digits divisible by 4, and ends in even digit (for 2).

Are there any shortcuts for finding numbers divisible by 10, 4, and 2?

Yes! Since 10 = 2 × 5, any number divisible by both 10 and 4 must be divisible by their LCM (Least Common Multiple), which is 20. So look for multiples of 20!

Why isn't 30 the right answer?

30 is tricky! It ends in 0 (divisible by 10 and 2), but the last two digits are 30. Since $30 ÷ 4 = 7.5$ , it's not divisible by 4. Remember: all conditions must be met!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Division - Advanced questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime