Start from absolute scratch with number classifications, place vs face value, fast divisibility checks, and 15-second Vedic mental math tricks.
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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.
