What is Divisibility?

S3-SA4-0355

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

Divisibility means that one number can be divided by another number without leaving any remainder. If a division results in a whole number (no fractions or decimals), then the first number is divisible by the second.

Simple Example

Quick Example

Imagine you have 10 ladoos and you want to share them equally among 5 friends. Each friend gets 2 ladoos, and no ladoos are left over. So, 10 is divisible by 5.

Worked Example

Step-by-Step

Let's check if 24 is divisible by 6.

1. Start by dividing 24 by 6.

---2. Perform the division: 24 ÷ 6.

---3. When you divide 24 by 6, the answer (quotient) is 4.

---4. Check the remainder: 6 multiplied by 4 is exactly 24, so the remainder is 0.

---5. Since the remainder is 0, 24 is divisible by 6.

Answer: Yes, 24 is divisible by 6.

Why It Matters

Understanding divisibility is super important in fields like Computer Science and Cryptography for creating secure codes and efficient programs. Even data scientists use it to organize information. It's a foundational skill for anyone wanting to work with numbers, from engineers to economists!

Common Mistakes

MISTAKE: Thinking a number is divisible even if there's a remainder. For example, saying 10 is divisible by 3 because you get 3.33. | CORRECTION: Divisibility only applies when the remainder is exactly zero. 10 is NOT divisible by 3.

MISTAKE: Confusing division with divisibility. All numbers can be divided, but not all are divisible by another specific number. | CORRECTION: Division is the operation, divisibility is a property (whether the division results in a zero remainder).

MISTAKE: Not checking the remainder carefully. Sometimes students rush and make a calculation error. | CORRECTION: Always double-check your multiplication (divisor x quotient) to ensure it equals the dividend and confirms a zero remainder.

Practice Questions

Try It Yourself

QUESTION: Is 35 divisible by 7? | ANSWER: Yes

QUESTION: A class has 42 students. Can they be divided equally into groups of 5? Is 42 divisible by 5? | ANSWER: No, 42 is not divisible by 5.

QUESTION: You have 60 rupees. Can you buy an exact number of ice creams if each costs 8 rupees? Is 60 divisible by 8? | ANSWER: No, 60 is not divisible by 8.

MCQ

Quick Quiz

Which of the following numbers is divisible by 4?

The Correct Answer Is:

32 divided by 4 gives a quotient of 8 with a remainder of 0, so 32 is divisible by 4. The other options leave a remainder when divided by 4.

Real World Connection

In the Real World

When you buy groceries online using apps like BigBasket or Swiggy Instamart, the system often calculates if your total bill is divisible by certain payment amounts for discounts or offers. For example, if there's a discount for bills divisible by 500 rupees, the app uses divisibility to check if you qualify!

Key Vocabulary

Key Terms

DIVIDEND: The number being divided | DIVISOR: The number by which another number is divided | QUOTIENT: The result of a division | REMAINDER: The amount left over after a division

What's Next

What to Learn Next

Great job learning about divisibility! Next, you should explore 'Divisibility Rules'. These are clever shortcuts that help you quickly check if a number is divisible by another number without actually doing the full division. It's like a superpower for numbers!