Real Numbers
Madhya Pradesh Board · Class 10 · Mathematics
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Explore the full setFind the prime factorisation of 32760.
Answer
Step 1: Break 32760 into prime factors. Step 2: 32760 = 2 × 2 × 2 × 3 × 3 × 5 × 7 × 13. Step 3: Write repeated primes using powers. Answer: 32760 = 2^3 × 3^2 × 5 × 7 × 13. Check: 2^3 = 8 and 3^2 = 9, …
32760 का अभाज्य गुणनखंडन ज्ञात कीजिए।
Answer
चरण 1: 32760 को अभाज्य गुणनखंडों में तोड़िए। चरण 2: 32760 = 2 × 2 × 2 × 3 × 3 × 5 × 7 × 13. चरण 3: दोहराए गए अभाज्य संख्याओं को घातों के रूप में लिखिए। उत्तर: 32760 = 2^3 × 3^2 × 5 × 7 × 13. जाँच: 2^3…
Why is prime factorisation of a composite number unique, apart from order?
Answer
A composite number can be written as a product of primes in only one way, except that the order of the primes may change. Example: 2 × 3 × 5 × 7 and 3 × 5 × 7 × 2 give the same factorisation. So, chan…
संयोज्य संख्या का अभाज्य गुणनखंडन, क्रम को छोड़कर, अद्वितीय क्यों होता है?
Answer
एक संयोज्य संख्या को अभाज्य संख्याओं के गुणनफल के रूप में केवल एक ही तरह से लिखा जा सकता है, सिवाय इसके कि अभाज्य संख्याओं का क्रम बदल सकता है। उदाहरण: 2 × 3 × 5 × 7 और 3 × 5 × 7 × 2 एक ही गुणनखंडन दे…
Find the HCF and LCM of 6 and 20 by prime factorisation.
Answer
Step 1: Write prime factors. 6 = 2^1 × 3^1 20 = 2^2 × 5^1 Step 2: HCF uses the smallest power of each common prime factor. Common prime factor is 2, smallest power is 2^1. So, HCF(6, 20) = 2. Step 3: …
6 और 20 का HCF और LCM अभाज्य गुणनखंडन द्वारा ज्ञात कीजिए।
Answer
चरण 1: अभाज्य गुणनखंड लिखिए। 6 = 2^1 × 3^1 20 = 2^2 × 5^1 चरण 2: HCF प्रत्येक उभयनिष्ठ अभाज्य गुणनखंड की सबसे छोटी घात का उपयोग करता है। उभयनिष्ठ अभाज्य गुणनखंड 2 है, और सबसे छोटी घात 2^1 है। इसलिए, H…
When do you use the relation HCF(a, b) × LCM(a, b) = a × b?
Answer
Use this only for two positive integers. Formula: HCF(a, b) × LCM(a, b) = a × b. Example: For 6 and 20, HCF = 2 and LCM = 60. So, 2 × 60 = 120 and 6 × 20 = 120. Both sides are equal, so the relation i…
आप HCF(a, b) × LCM(a, b) = a × b संबंध का उपयोग कब करते हैं?
Answer
इसका उपयोग केवल दो धनात्मक पूर्णांकों के लिए करें। सूत्र: HCF(a, b) × LCM(a, b) = a × b. उदाहरण: 6 और 20 के लिए, HCF = 2 और LCM = 60. इसलिए, 2 × 60 = 120 और 6 × 20 = 120. दोनों पक्ष बराबर हैं, इसलिए स…
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