What is the Test for Divisibility by 3?

S3-SA4-0038

Grade Level:

Class 6

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

Definition

What is it?

The Test for Divisibility by 3 is a quick way to check if a number can be divided by 3 without leaving any remainder. You just need to add up all the digits of the number. If the sum of the digits is divisible by 3, then the original number is also divisible by 3.

Simple Example

Quick Example

Imagine you have 12 laddoos and you want to share them equally among 3 friends. To check if 12 is divisible by 3, add its digits: 1 + 2 = 3. Since 3 is divisible by 3, you know 12 laddoos can be shared equally among 3 friends (each gets 4).

Worked Example

Step-by-Step

Let's check if the number 546 is divisible by 3.

Step 1: Write down the number: 546.

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Step 2: Add all the digits of the number: 5 + 4 + 6.

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Step 3: Calculate the sum: 5 + 4 + 6 = 15.

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Step 4: Now, check if this sum (15) is divisible by 3. You know that 3 x 5 = 15, so 15 is divisible by 3.

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Step 5: Since the sum of the digits (15) is divisible by 3, the original number (546) is also divisible by 3.

Answer: Yes, 546 is divisible by 3.

Why It Matters

Understanding divisibility rules helps you work with numbers faster, which is super useful in fields like Computer Science for writing efficient code or in Data Science for quickly sorting large datasets. Engineers use these concepts for calculations, and even in Cryptography, divisibility plays a role in secure communication.

Common Mistakes

MISTAKE: Only checking the last digit to see if it's divisible by 3. | CORRECTION: The divisibility rule for 3 requires you to sum ALL the digits, not just look at the last one. The last digit rule is for numbers like 2, 5, or 10.

MISTAKE: Forgetting to check if the sum of the digits is divisible by 3, and just assuming the original number is divisible if the sum is large. | CORRECTION: After summing the digits, you MUST perform the divisibility check on that sum. For example, if the sum is 17, 17 is not divisible by 3, so the original number isn't either.

MISTAKE: Making calculation errors when adding the digits, especially for larger numbers. | CORRECTION: Double-check your addition of the digits. If the sum is a big number, you can even apply the divisibility rule again to the sum itself (e.g., if sum is 27, add 2+7=9, which is divisible by 3).

Practice Questions

Try It Yourself

QUESTION: Is 78 divisible by 3? | ANSWER: Yes

QUESTION: A cricket team scored 215 runs. Is 215 divisible by 3? | ANSWER: No

QUESTION: Your mobile bill for the month is Rs. 12,345. Can this amount be divided exactly into 3 equal parts (perhaps for a family plan)? | ANSWER: No

MCQ

Quick Quiz

Which of the following numbers is divisible by 3?

125

347

612

809

The Correct Answer Is:

For 612, the sum of digits is 6 + 1 + 2 = 9. Since 9 is divisible by 3, 612 is divisible by 3. For the other options, the sum of digits is not divisible by 3.

Real World Connection

In the Real World

Imagine a delivery service like Zepto or Dunzo planning routes. If they have 3 drivers and need to divide 123 packages equally, they'd quickly check if 1+2+3=6, which is divisible by 3. This helps them balance workload efficiently without actually doing long division.

Key Vocabulary

Key Terms

DIVISIBILITY: The ability of one number to be divided by another without a remainder. | REMAINDER: The amount left over after a division when the divisor does not perfectly divide the dividend. | SUM: The result of adding two or more numbers. | DIGIT: A single symbol used to make numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).

What's Next

What to Learn Next

Great job learning the divisibility test for 3! Next, you should explore divisibility tests for other numbers like 4, 6, and 9. These rules build on what you've learned and will make you even faster at number crunching!