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What is Divisibility by 3?
Grade Level:
Class 4
Maths, Computing, AI
Definition
What is it?
Divisibility by 3 means that when you divide a number by 3, there is no remainder left. In simpler words, the number can be split into three equal parts without anything left over. It's a quick way to check if a number is a multiple of 3.
Simple Example
Quick Example
Imagine you have 15 ladoos to share equally among 3 friends. Each friend gets 5 ladoos, and no ladoos are left. So, 15 is divisible by 3. If you had 16 ladoos, you couldn't share them equally among 3 friends without having some left over, so 16 is not divisible by 3.
Worked Example
Step-by-Step
Let's check if the number 258 is divisible by 3.
Step 1: Add up all the digits in the number. For 258, the digits are 2, 5, and 8.
---Step 2: Sum of the digits = 2 + 5 + 8 = 15.
---Step 3: Now, check if this sum (15) is divisible by 3. You can either divide 15 by 3 or recall your 3-times table.
---Step 4: 15 ÷ 3 = 5. Since 15 is perfectly divisible by 3 (with no remainder), the original number 258 is also divisible by 3.
Answer: Yes, 258 is divisible by 3.
Why It Matters
Understanding divisibility rules helps you work with numbers faster, which is super useful in Maths for simplifying fractions or finding factors. In Computing, these rules are used in algorithms for data processing and error checking. Even AI systems use number properties to solve complex problems, making calculations more efficient.
Common Mistakes
MISTAKE: Dividing the number by 3 directly and stopping if there's a remainder. | CORRECTION: The trick is to sum the digits first, then check if that sum is divisible by 3. This is much faster for larger numbers.
MISTAKE: Only checking the last digit. | CORRECTION: Divisibility by 3 is NOT about the last digit (like divisibility by 2, 5, or 10). It's always about the sum of ALL the digits.
MISTAKE: Forgetting to add all digits for multi-digit sums (e.g., if sum is 12, then checking 12 not 1+2). | CORRECTION: If the sum of digits is a two-digit number (like 12 or 21), you can sum its digits again (1+2=3 or 2+1=3) to check if it's divisible by 3.
Practice Questions
Try It Yourself
QUESTION: Is the number 72 divisible by 3? | ANSWER: Yes (7+2=9, and 9 is divisible by 3)
QUESTION: A cricket team scored 135 runs. Can these runs be divided equally into groups of 3? | ANSWER: Yes (1+3+5=9, and 9 is divisible by 3)
QUESTION: Your mobile data pack gives you 472 MB. Can this total data be divided perfectly into three equal parts for three different apps? | ANSWER: No (4+7+2=13, and 13 is not divisible by 3)
MCQ
Quick Quiz
Which of these numbers is divisible by 3?
52
74
81
95
The Correct Answer Is:
C
For 81, the sum of digits is 8+1=9. Since 9 is divisible by 3 (9 ÷ 3 = 3), 81 is divisible by 3. For the other options, the sum of digits (5+2=7, 7+4=11, 9+5=14) is not divisible by 3.
Real World Connection
In the Real World
Imagine a shopkeeper in a busy market counting their daily earnings. If the total amount of money earned is Rs. 1245, they might quickly check if it's divisible by 3 to see if it can be easily split into three equal shares for partners or for different expense categories. They would sum the digits: 1+2+4+5 = 12. Since 12 is divisible by 3, Rs. 1245 is also divisible by 3.
Key Vocabulary
Key Terms
DIVISIBILITY: The ability of one number to be divided by another number without leaving a remainder. | REMAINDER: The amount left over after division. | SUM: The result of adding two or more numbers. | DIGIT: A single symbol used to make up numbers (e.g., in 258, 2, 5, and 8 are digits). | MULTIPLE: A number that can be divided by another number without a remainder.
What's Next
What to Learn Next
Great job understanding divisibility by 3! Next, you should explore 'Divisibility by 6'. It builds directly on what you learned here, as a number divisible by 6 must also be divisible by both 2 and 3. Keep practicing, it makes you a number wizard!
