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Common questions and clear answers for this topic.
Number System covers Natural Numbers (1,2,3), Whole Numbers (0,1,2,3), Integers, Rational Numbers (p/q form), Irrational Numbers (like pi and root 2), and Real Numbers. For competitive exams like SSC CGL and IBPS, focus on: divisibility rules, LCM and HCF, factors, prime numbers, and unit digit calculations.
Divisibility rules: Divisible by 2 - last digit even. By 3 - sum of digits divisible by 3. By 4 - last two digits divisible by 4. By 5 - last digit 0 or 5. By 6 - divisible by both 2 and 3. By 8 - last three digits divisible by 8. By 9 - sum of digits divisible by 9. By 11 - difference of alternating digit sums divisible by 11. Mastering these rules helps solve Number System questions faster in competitive exams.
LCM (Least Common Multiple) is the smallest number divisible by all given numbers. HCF (Highest Common Factor) is the largest number that divides all given numbers. Methods: For HCF - prime factorization or Euclidean algorithm. For LCM - prime factorization. Key relationship: LCM x HCF = Product of two numbers (only for two numbers). LCM and HCF questions appear in all major competitive exams.
Unit digits follow cyclicity patterns: For 2 - cycle is 2,4,8,6 (length 4). For 3 - cycle is 3,9,7,1 (length 4). For 4 - cycle is 4,6 (length 2). For 7 - cycle is 7,9,3,1 (length 4). For 8 - cycle is 8,4,2,6 (length 4). For 0,1,5,6 - unit digit is always 0,1,5,6 regardless of power. Divide the power by the cycle length and use the remainder to find the unit digit.
Prime numbers up to 100 (25 total): 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. All other numbers (except 1) are composite. 1 is neither prime nor composite. 2 is the only even prime. To check if a number N is prime, check divisibility only up to the square root of N.
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