What is Divisibility by 10?

S1-SA1-0167

Grade Level:

Class 3

Maths, Computing, AI

Definition

What is it?

Divisibility by 10 means a number can be divided by 10 without leaving any remainder. A simple trick to check for divisibility by 10 is to look at the last digit of the number.

Simple Example

Quick Example

Imagine you have 70 ladoos and you want to pack them into boxes, with 10 ladoos in each box. You can pack exactly 7 boxes (70 ÷ 10 = 7) with no ladoos left over. This means 70 is divisible by 10.

Worked Example

Step-by-Step

Let's check if 145 is divisible by 10.

Step 1: Look at the last digit of the number 145.
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Step 2: The last digit is 5.
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Step 3: For a number to be divisible by 10, its last digit must be 0.
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Step 4: Since 5 is not 0, 145 is NOT divisible by 10.
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Step 5: If you divide 145 by 10, you get 14 with a remainder of 5. So, 145 is not perfectly divisible by 10.

Why It Matters

Understanding divisibility rules helps you quickly estimate and solve problems in Maths. In Computing and AI, these rules are used in algorithms for data processing and pattern recognition, making calculations faster. It's useful for careers in software development, data science, and even financial analysis.

Common Mistakes

MISTAKE: Thinking any number ending in a multiple of 10 (like 20, 30) is divisible by 10. | CORRECTION: Only the last digit matters. If the last digit is 0, it's divisible by 10. For example, 120 is divisible by 10 because it ends in 0, not because 20 is a multiple of 10.

MISTAKE: Confusing divisibility by 10 with divisibility by 2 or 5. | CORRECTION: Divisibility by 2 means the last digit is 0, 2, 4, 6, or 8. Divisibility by 5 means the last digit is 0 or 5. For divisibility by 10, the last digit MUST be 0.

MISTAKE: Trying to perform long division every time to check. | CORRECTION: Remember the simple rule: if the last digit is 0, it's divisible by 10. This is a shortcut to save time.

Practice Questions

Try It Yourself

QUESTION: Is 230 divisible by 10? | ANSWER: Yes

QUESTION: Which of these numbers is NOT divisible by 10: 40, 105, 780, 900? | ANSWER: 105

QUESTION: A shopkeeper has 345 candies. Can she pack them into bags of 10 candies each without any candies left over? | ANSWER: No, because 345 ends in 5, not 0.

MCQ

Quick Quiz

Which of the following numbers is divisible by 10?

101

270

342

The Correct Answer Is:

A number is divisible by 10 if its last digit is 0. Only 270 has 0 as its last digit. The other numbers end in 5, 1, or 2, so they are not divisible by 10.

Real World Connection

In the Real World

When you buy items at a local kirana store and the bill total is ₹250, the shopkeeper can easily calculate that it's 25 times ₹10 notes. Also, in computer programming, when you need to group data into batches of 10 (like 10 photos per album page), divisibility by 10 checks help ensure no photos are left out.

Key Vocabulary

Key Terms

DIVISIBILITY: The ability of one number to be divided by another without a remainder. | REMAINDER: The amount left over after division. | LAST DIGIT: The rightmost digit of a number. | MULTIPLE: A number that can be divided by another number a certain number of times without a remainder.

What's Next

What to Learn Next

Great job understanding divisibility by 10! Next, you can explore 'Divisibility by 2 and 5' to see how these rules are similar and different. This will help you become even faster at mental math and solving problems.