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What is the Test for Divisibility by 12?
Grade Level:
Class 6
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
The test for divisibility by 12 helps us quickly check if a large number can be divided by 12 without leaving any remainder. A number is divisible by 12 if it is divisible by both 3 AND 4.
Simple Example
Quick Example
Imagine you have 24 laddoos and want to pack them into boxes, with 12 laddoos in each box. Since 24 is divisible by 3 (2+4=6, which is divisible by 3) and 24 is also divisible by 4 (last two digits '24' are divisible by 4), 24 is divisible by 12. You can perfectly fill 2 boxes!
Worked Example
Step-by-Step
Let's check if the number 576 is divisible by 12.
Step 1: Check for divisibility by 3. Sum of digits = 5 + 7 + 6 = 18.
---Step 2: Is 18 divisible by 3? Yes, 18 / 3 = 6. So, 576 is divisible by 3.
---Step 3: Now, check for divisibility by 4. Look at the last two digits of 576, which are 76.
---Step 4: Is 76 divisible by 4? Yes, 76 / 4 = 19. So, 576 is divisible by 4.
---Step 5: Since 576 is divisible by BOTH 3 and 4, it is divisible by 12.
---Answer: Yes, 576 is divisible by 12.
Why It Matters
Understanding divisibility rules is like having a superpower for numbers, making calculations faster in fields like Computer Science and Engineering. It helps in quickly finding patterns, which is useful for Data Scientists analyzing large datasets or Cryptographers creating secure codes.
Common Mistakes
MISTAKE: Checking only for divisibility by 3 OR only by 4. | CORRECTION: Remember, for a number to be divisible by 12, it MUST be divisible by BOTH 3 and 4.
MISTAKE: Confusing the divisibility rule for 4 (last two digits) with the rule for 3 (sum of digits). | CORRECTION: Always apply the correct rule for each factor: sum of digits for 3, and last two digits for 4.
MISTAKE: Assuming a number is divisible by 12 if it ends in an even number (like 2, 4, 6, 8, 0). | CORRECTION: While divisibility by 4 implies an even number, it's not enough. You still need to check the last two digits for divisibility by 4 and the sum of digits for divisibility by 3.
Practice Questions
Try It Yourself
QUESTION: Is 108 divisible by 12? | ANSWER: Yes
QUESTION: Check if 732 is divisible by 12. Show your steps. | ANSWER: Divisible by 3 (7+3+2=12, 12/3=4). Divisible by 4 (32/4=8). Yes, 732 is divisible by 12.
QUESTION: Find the smallest 3-digit number that is divisible by 12. | ANSWER: 108
MCQ
Quick Quiz
Which of these numbers is NOT divisible by 12?
144
216
308
360
The Correct Answer Is:
C
144, 216, and 360 are all divisible by both 3 and 4. 308 is divisible by 4 (08/4=2) but not by 3 (3+0+8=11, which is not divisible by 3).
Real World Connection
In the Real World
In a factory that packs samosas, if they need to arrange samosas in trays of 12, knowing divisibility by 12 helps them quickly see if a batch of 500 samosas can be perfectly packed without any leftovers. This prevents waste and makes packing efficient, just like how logistics companies use similar concepts for delivery planning.
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. | FACTOR: A number that divides another number exactly. | COMPOSITE NUMBER: A number that has more than two factors (e.g., 12 has factors 1, 2, 3, 4, 6, 12).
What's Next
What to Learn Next
Great job learning about divisibility by 12! Next, you can explore divisibility rules for other numbers like 6, 8, or even 9. This will further strengthen your number sense and make you a master of mental math!
