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What is Divisibility by 6?
Grade Level:
Class 5
Maths, Computing, AI
Definition
What is it?
Divisibility by 6 means that a number can be divided by 6 without leaving any remainder. A number is divisible by 6 if it is divisible by both 2 and 3.
Simple Example
Quick Example
Imagine you have 18 laddoos. Can you share them equally among 6 friends without any laddoos left over? Yes, each friend gets 3 laddoos (18 / 6 = 3). So, 18 is divisible by 6.
Worked Example
Step-by-Step
Let's check if the number 54 is divisible by 6.
---Step 1: Check divisibility by 2. A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8). The last digit of 54 is 4, which is an even number. So, 54 is divisible by 2.
---Step 2: Check divisibility by 3. A number is divisible by 3 if the sum of its digits is divisible by 3. For 54, the sum of digits is 5 + 4 = 9. Since 9 is divisible by 3 (9 / 3 = 3), 54 is divisible by 3.
---Step 3: Since 54 is divisible by both 2 and 3, it is divisible by 6.
---Answer: Yes, 54 is divisible by 6.
Why It Matters
Understanding divisibility rules helps you quickly solve problems in Maths. In Computing and AI, these rules are used in algorithms for data sorting and encryption. It's like a secret shortcut that makes calculations faster for data analysts and software engineers.
Common Mistakes
MISTAKE: Only checking divisibility by 2, or only by 3. For example, thinking 10 is divisible by 6 because it's divisible by 2. | CORRECTION: A number MUST be divisible by BOTH 2 and 3 to be divisible by 6.
MISTAKE: Confusing the rule for 6 with other divisibility rules. For example, thinking the last digit must be 6. | CORRECTION: Remember the 'two-in-one' rule: divisible by 2 AND divisible by 3.
MISTAKE: Making calculation errors when summing digits for the divisibility by 3 test. For example, for 246, summing 2+4+6=13, and thinking 13 is divisible by 3. | CORRECTION: Double-check your sum of digits. 2+4+6 = 12, and 12 is divisible by 3.
Practice Questions
Try It Yourself
QUESTION: Is the number 72 divisible by 6? | ANSWER: Yes
QUESTION: Which of these numbers is NOT divisible by 6: 30, 42, 50, 66? | ANSWER: 50
QUESTION: A shopkeeper has 108 ladoos. Can he pack them into boxes of 6 without any ladoos left over? Show your working. | ANSWER: Yes. 108 is even (last digit 8, divisible by 2). Sum of digits 1+0+8 = 9, which is divisible by 3. Since it's divisible by both 2 and 3, it's divisible by 6.
MCQ
Quick Quiz
Which of the following numbers is divisible by 6?
26
34
48
52
The Correct Answer Is:
C
48 is divisible by 2 (ends in 8) and divisible by 3 (4+8=12, which is divisible by 3). The other options fail either the divisibility by 2 or by 3 test.
Real World Connection
In the Real World
Imagine you're a delivery driver for a company like Zepto or Blinkit. You need to deliver 48 packages, and your delivery vehicle can carry exactly 6 packages per trip. Knowing divisibility by 6 helps you quickly figure out if you'll have full trips or leftover packages.
Key Vocabulary
Key Terms
DIVISIBILITY: The ability of one number to be divided by another number without a remainder | REMAINDER: The amount left over after division | EVEN NUMBER: A number that is divisible by 2 | SUM OF DIGITS: The total you get when you add all the individual digits of a number together
What's Next
What to Learn Next
Great job learning about divisibility by 6! Next, you can explore divisibility rules for other numbers like 4, 8, 9, and 11. These rules are like secret keys that unlock faster calculations and make complex math problems much simpler!
