Divisibility Rules: Does Divisibility by 10 Imply Divisibility by 2?

Divisibility Rules with Factor Relationships

If a number is divisible by 10, is it also therefore divisible by 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 If a number is divisible by 10, is it also divisible by 2?
00:03 Let's take any number and divide it by 10
00:11 Let's break down 10 into factors 2 and 5
00:15 Therefore, any number divisible by 10 must also be divisible by 2
00:23 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

If a number is divisible by 10, is it also therefore divisible by 2?

2

Step-by-step solution

The answer is yes - every number that is divisible by 10 is divisible by 2.

This can be learned through the divisibility rules of each number.

We know that to identify a number divisible by 10, we need to examine its ones digit,

only numbers whose ones digit is 0 are divisible by 10,

for example: 30, 510, 15610

We know that numbers whose ones digit is 0 are actually even numbers,

and even numbers are divisible by 2 without a remainder.

Therefore, we can be certain - every number that is divisible by 10 is also divisible by 2.

It's important to understand that this is not necessarily true in reverse, not every number that is divisible by 2 is also divisible by 10!

3

Final Answer

Yes.

Key Points to Remember

Essential concepts to master this topic
  • Rule: If divisible by 10, then always divisible by 2
  • Technique: Check ones digit: if 0, then divisible by both 10 and 2
  • Check: Test with 30: 30÷10=3, 30÷2=15, both whole numbers ✓

Common Mistakes

Avoid these frequent errors
  • Thinking divisibility works both ways equally
    Don't assume if divisible by 2, then divisible by 10 = wrong logic! Numbers like 6, 14, 22 are divisible by 2 but not by 10. Always remember: divisibility by 10 implies divisibility by 2, but not vice versa.

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 divisibility by 10 always mean divisibility by 2?

+

Because 10 = 2 × 5! If a number is divisible by 10, it contains both 2 and 5 as factors. Since it has 2 as a factor, it must be divisible by 2.

Are there other examples like this with different numbers?

+

Yes! If a number is divisible by 12, it's also divisible by 3, 4, and 6 because 12 = 3 × 4. Any factor of the divisor will also divide the number.

What's the pattern for numbers ending in 0?

+

All numbers ending in 0 are even numbers, which means they're automatically divisible by 2. Examples: 10, 20, 30, 100, 250 - all even!

If 24 is divisible by 2, is it divisible by 10?

+

No! Just because 24 ÷ 2 = 12, doesn't mean 24 ÷ 10 works. 24 ÷ 10 = 2.4, not a whole number. The relationship only works one way.

How can I remember which way this rule works?

+

Think of it like size: if you can fit into a smaller box (divisible by 10), you can definitely fit into a bigger box (divisible by 2). But fitting in the bigger box doesn't guarantee you fit in the smaller one!

🌟 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

More Questions

Click on any question to see the complete solution with step-by-step explanations