Is 10 Divisible by 4? A Simple Arithmetic Test

Q: What does it mean for a number to be divisible by another?

A number is divisible by another number when you can divide them with no remainder left over. For example, 12 ÷ 4 = 3 with no remainder, so 12 is divisible by 4.

Q: Why isn't 10 divisible by 4 if I get 2.5?

The decimal 2.5 tells us there's a leftover part! When we divide 10 by 4, we get 2 whole groups with 2 left over. Only whole number results with zero remainder show divisibility.

Q: How do I find the remainder without a calculator?

Use long division or think: What's the biggest multiple of 4 that fits in 10? That's 8 (4×2). So 10 - 8 = 2 remainder.

Q: Is there a quick trick to test divisibility by 4?

Yes! For divisibility by 4, look at the last two digits. If the last two digits form a number divisible by 4, then the whole number is. Since 10 ends in 10, and 10 ÷ 4 has remainder 2, it's not divisible.

Q: Can I use multiplication to check my answer?

Absolutely! Multiply the quotient by the divisor and add the remainder: 2 × 4 + 2 = 10. If this equals your original number, you did it right!

Divisibility Testing with Remainder Calculation

Is the number 10 divisible by 4?

❤️ 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 Is the number divisible by 4?

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

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

00:16 We can see that the number is not divisible by 4

00:21 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

Is the number 10 divisible by 4?

Step-by-step solution

To determine if the number 10 is divisible by 4, follow these steps:

Step 1: Perform Division
Divide 10 by 4. Calculate $\frac{10}{4}$ .
Step 2: Check Result for Integer
If $\frac{10}{4} = 2.5$ , the result is not an integer.
Step 3: Confirm Remainder
Determine the remainder when 10 is divided by 4. $10 \div 4$ gives a quotient of 2 and a remainder of 2.
Step 4: Conclusion on Divisibility
Since there is a remainder, 10 is not divisible by 4.

Therefore, the number 10 is not divisible by 4. The correct answer is No.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: A number is divisible by another if remainder equals zero
Technique: Calculate $10 \div 4 = 2$ remainder 2
Check: Verify using multiplication: 4 × 2 + 2 = 10 ✓

Common Mistakes

Avoid these frequent errors

Confusing decimal quotients with divisibility
Don't assume a decimal result like $\frac{10}{4} = 2.5$ means the number is divisible! The decimal shows there's a remainder. Always check if the division result is a whole number with zero remainder.

Practice Quiz

Test your knowledge with interactive questions

Is the number 43 divisible by 4?

FAQ

Everything you need to know about this question

What does it mean for a number to be divisible by another?

A number is divisible by another number when you can divide them with no remainder left over. For example, 12 ÷ 4 = 3 with no remainder, so 12 is divisible by 4.

Why isn't 10 divisible by 4 if I get 2.5?

The decimal 2.5 tells us there's a leftover part! When we divide 10 by 4, we get 2 whole groups with 2 left over. Only whole number results with zero remainder show divisibility.

How do I find the remainder without a calculator?

Use long division or think: What's the biggest multiple of 4 that fits in 10? That's 8 (4×2). So 10 - 8 = 2 remainder.

Is there a quick trick to test divisibility by 4?

Yes! For divisibility by 4, look at the last two digits. If the last two digits form a number divisible by 4, then the whole number is. Since 10 ends in 10, and 10 ÷ 4 has remainder 2, it's not divisible.

Can I use multiplication to check my answer?

Absolutely! Multiply the quotient by the divisor and add the remainder: 2 × 4 + 2 = 10. If this equals your original number, you did it right!

🌟 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