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What is a Divisible Number?
Grade Level:
Class 6
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
A number is called 'divisible' by another number if, when you divide the first number by the second, the remainder is zero. It means the second number goes into the first number a whole number of times, without anything left over.
Simple Example
Quick Example
Imagine you have 10 laddoos and you want to share them equally among 5 friends. Each friend gets 2 laddoos, and there are no laddoos left. So, 10 is divisible by 5.
Worked Example
Step-by-Step
Let's check if 24 is divisible by 4.
Step 1: Write down the division problem: 24 ÷ 4.
---Step 2: Perform the division. You can think of how many times 4 goes into 24.
---Step 3: We know that 4 x 6 = 24.
---Step 4: So, 24 divided by 4 is 6.
---Step 5: The remainder is 0 (24 - 24 = 0).
---Answer: Since the remainder is 0, 24 is divisible by 4.
Why It Matters
Understanding divisibility is key in many fields! In computer science, it helps in writing efficient code and understanding data structures. Engineers use it for calculations, and even in cryptography, it forms the basis of secure communication. This simple idea can open doors to exciting careers in technology and science!
Common Mistakes
MISTAKE: Thinking a number is divisible even if there's a remainder | CORRECTION: A number is only divisible if the remainder after division is exactly zero.
MISTAKE: Confusing 'divisible by' with 'can be divided by' | CORRECTION: Any number can be divided by another (except by zero), but it's only 'divisible by' if the division results in a whole number with no remainder.
MISTAKE: Only checking with small numbers and assuming divisibility | CORRECTION: Always perform the full division or use divisibility rules to confirm if a number is truly divisible, especially for larger numbers.
Practice Questions
Try It Yourself
QUESTION: Is 35 divisible by 7? | ANSWER: Yes, because 35 ÷ 7 = 5 with a remainder of 0.
QUESTION: A class has 42 students. Can they be divided into groups of 5 with no students left over? | ANSWER: No, because 42 ÷ 5 = 8 with a remainder of 2. So, 42 is not divisible by 5.
QUESTION: You have 75 rupees. Can you buy an exact number of ice creams if each ice cream costs 8 rupees? Explain why or why not. | ANSWER: No, because 75 ÷ 8 = 9 with a remainder of 3. You can buy 9 ice creams, but you will have 3 rupees left, so 75 is not divisible by 8.
MCQ
Quick Quiz
Which of these numbers is divisible by 6?
25
32
48
50
The Correct Answer Is:
C
48 divided by 6 is exactly 8, with no remainder. For the other options, 25 ÷ 6 leaves a remainder of 1, 32 ÷ 6 leaves a remainder of 2, and 50 ÷ 6 leaves a remainder of 2.
Real World Connection
In the Real World
When you book train tickets online and want to split the fare equally among your friends, you're using divisibility. If the total fare is Rs 1200 and there are 4 friends, each pays Rs 300 because 1200 is divisible by 4. If the fare was Rs 1205, it wouldn't be perfectly divisible, and someone would have to pay extra or less.
Key Vocabulary
Key Terms
DIVISOR: The number by which another number is divided | DIVIDEND: The number being divided | QUOTIENT: The result of division | REMAINDER: The amount left over after division | WHOLE NUMBER: A number without fractions or decimals (0, 1, 2, 3...)
What's Next
What to Learn Next
Great job understanding divisible numbers! Now that you know this, you're ready to learn about 'Divisibility Rules'. These are clever shortcuts that help you quickly check if a number is divisible by 2, 3, 5, 10, and more, without actually doing the long division!
