Divisibility Rules
Divisibility rules help solve aptitude questions faster by checking divisibility through simple digit-based tests instead of lengthy calculations.
Fundamental Principles
Divisibility
A number is divisible by another number if the remainder is zero after division.
Divisibility Rule
A shortcut method used to determine whether a number can be divided exactly by another number.
Essential Formulation Tips
- Always start with simple rules such as 2, 5, and 10.
- For 3 and 9, use the sum of digits.
- For 4 and 8, focus on the last few digits only.
- Practice common divisibility tests to improve speed.
Shortcut Execution Techniques
- Divisible by 2 → Last digit is even.
- Divisible by 3 → Sum of digits is divisible by 3.
- Divisible by 4 → Last two digits form a number divisible by 4.
- Divisible by 5 → Last digit is 0 or 5.
- Divisible by 6 → Number is divisible by both 2 and 3.
- Divisible by 8 → Last three digits form a number divisible by 8.
- Divisible by 9 → Sum of digits is divisible by 9.
- Divisible by 10 → Last digit is 0.
Contextual Inquiries (FAQs)
Q: How do I check divisibility by 3?
A: Add all digits. If the sum is divisible by 3, the number is divisible by 3.
Q: How do I check divisibility by 4?
A: Check whether the last two digits form a number divisible by 4.
Q: Why are divisibility rules important in aptitude exams?
A: They help solve HCF, LCM, factors, and number system questions quickly.
Example Breakdown: Checking Divisibility by 4
One of the most commonly used divisibility shortcuts.Take the last two digits: 28
28 ÷ 4 = 7
Since 28 is divisible by 4, 4728 is divisible by 4.
Example Breakdown: Checking Divisibility by 3
Useful for quickly eliminating options in MCQs.Add the digits: 5 + 6 + 4 = 15
15 is divisible by 3
Therefore, 564 is divisible by 3.
Example Breakdown: Checking Divisibility by 9
A favorite question type in aptitude exams.Add the digits: 7 + 2 + 9 = 18
18 is divisible by 9
Therefore, 729 is divisible by 9.
Set 1: Basics of 2, 5, and 10
Fundamental rules for ending digits.
Q1. Which of these is divisible by 2?
Q2. Is 55 divisible by 5?
Q3. Which is divisible by 10?
Q4. Is 42 divisible by 2?
Q5. Which is not divisible by 5?
Q6. Divisibility by 10 requires the number to end in:
Q7. Is 1000 divisible by 2?
Q8. Which number is divisible by 5?
Q9. Is 88 divisible by 2?
Q10. Which of these is NOT divisible by 10?