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यह Number System प्रश्न “1056 में सबसे छोटी कौन-सी संख्या जोड़ी जाए ताकि योग 23 से पूर्णतः विभाजित हो जाए?” के लिए सही interpretation और stepwise calculation विकसित करता है।
“1056 में सबसे छोटी कौन-सी संख्या जोड़ी जाए ताकि योग 23 से पूर्णतः विभाजित हो जाए?” को हल करते समय calculation शुरू करने से पहले सभी चिन्ह, brackets, powers और संख्यात्मक शर्तें ठीक रखें। प्रश्न के साथ उपलब्ध विशिष्ट गणना है: 1056 को 23 से भाग देने पर शेष 22 बचता है इसलिए 1 जोड़ने पर यह पूर्णतः विभाजित होगा।। शुद्धता के लिए संख्या के आकार से अलग उसकी mathematical structure पहचानें। प्रत्येक पंक्ति में केवल एक उचित परिवर्तन करें, common factors तभी cancel करें जब multiplication की अनुमति हो और समान priority वाली operations में left-to-right नियम रखें। जाँच के लिए चुने उत्तर को मूल relation में रखें अथवा equivalent fraction, factorisation या modular form से दोबारा calculation करें।
FAQ
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.
