Start from absolute scratch with number classifications, place vs face value, fast divisibility checks, and 15-second Vedic mental math tricks.
Study Zone is free for our students — you just need to log in with your WhatsApp number first.
Log in with WhatsApp →The first two chapters of every book are free once you're logged in. To open this one, request an unlock and we'll get back to you on WhatsApp.
Master the Indian vs International place value systems and number types.
📌 Place Value vs Face Value Formula
Face Value: The digit itself regardless of position (e.g. face value of 7 in 5,74,832 is 7).
Place Value: Digit × Position Value (e.g. place value of 7 is 7 × 10,000 = 70,000).
Difference Formula: Place Value − Face Value = 70,000 − 7 = 69,993.
📚 Core Number Classifications
Prime Numbers
Exactly 2 factors (1 & itself).
2, 3, 5, 7, 11... (2 is the only even prime)
Co-prime Numbers
HCF of the pair is 1.
(8, 9) are co-primes though both are composite.
Speed-check divisibility from 2 to 19 without long division.
📊 Fast Divisibility Rules Summary
| Divisor | Quick Test Rule | Example |
|---|---|---|
| 3 & 9 | Sum of digits is divisible by 3 or 9 | 4239: 4+2+3+9 = 18 (divisible by 9) |
| 4 & 8 | Last 2 digits (div by 4) or Last 3 digits (div by 8) | 5816: 816 ÷ 8 = 102 ✓ |
| 11 | Diff between (Odd place sum) and (Even place sum) is 0 or 11 | 9174: (9+7)-(1+4) = 11 ✓ |
Vedic Speed Hack: Multiplying by 11: Insert digit sum in between! e.g., 45 × 11 = 4 (4+5) 5 = 495.
Solve 30-second unit digit & remainder theorem questions for competitive exams.
🏆 Unit Digit Cyclicity Rules
Cyclicity 1 (0, 1, 5, 6): Unit digit never changes regardless of power (e.g. 5ⁿ ends in 5).
Cyclicity 2 (4, 9): 4ᵒᵈᵈ=4, 4ᵉᵛᵉⁿ=6; 9ᵒᵈᵈ=9, 9ᵉᵛᵉⁿ=1.
Cyclicity 4 (2, 3, 7, 8): Divide power by 4 and use remainder as exponent.
12 competitive questions testing divisibility, units digit, factors and remainder rules.