Number System – Advanced Tricks & Tough Problems
Build strong fundamentals with shortcuts and exam-level problems.
1. Divisibility Rules
Key Tricks:
- Divisible by 2 → Last digit even
- Divisible by 3 → Sum of digits divisible by 3
- Divisible by 5 → Last digit 0 or 5
- Divisible by 9 → Sum of digits divisible by 9
Example:
729 → 7 + 2 + 9 = 18 → divisible by 9
2. Remainder Shortcut
When dividing by 9, remainder = sum of digits mod 9
Example:
5678 ÷ 9
5 + 6 + 7 + 8 = 26 → 2 + 6 = 8
Answer = 8
3. Unit Digit Pattern
Use repeating cycles for powers
Example:
7² = 49 → 9
7³ = 343 → 3
7⁴ = 2401 → 1
7⁵ = 7
Cycle length = 4
Find unit digit of 7¹⁰⁰
100 mod 4 = 0 → Answer = 1
Tough Problems
Q1:
Find remainder when 12345 is divided by 9
Solution:
1 + 2 + 3 + 4 + 5 = 15 → 6
Answer = 6
Q2:
Find unit digit of 9¹⁰⁰
Solution:
Cycle of 9 → (9,1)
100 mod 2 = 0
Answer = 1
Q3:
Find number of factors of 36
Solution:
36 = 2² × 3²
(2+1)(2+1) = 9
Answer = 9
Exam Strategy
- Apply shortcuts instead of long calculations
- Memorize patterns for speed
- Practice factorization regularly
Shaktimatha Learning
Quantitative Aptitude • Bank Exams • Competitive Success
Quantitative Aptitude • Bank Exams • Competitive Success
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