Real Numbers — Flashcards
Punjab Board · Class 10 · Mathematics
25 flashcards for Real Numbers (Punjab Board Class 10 Mathematics) to test yourself on key terms and facts. Sample: "Express 140 as a product of its prime.
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Express 140 as a product of its prime factors
Answer
Step 1: Divide 140 by 2 → 70 Step 2: Divide 70 by 2 → 35 Step 3: Divide 35 by 5 → 7 Step 4: 7 is prime, so stop Prime factorization: 140 = 2² × 5 × 7 Verification: 4 × 5 × 7 = 140 ✓…
Find the prime factorization of 3825
Answer
Step 1: 3825 ÷ 3 = 1275 Step 2: 1275 ÷ 3 = 425 Step 3: 425 ÷ 5 = 85 Step 4: 85 ÷ 5 = 17 Step 5: 17 is prime Prime factorization: 3825 = 3² × 5² × 17 Verification: 9 × 25 × 17 = 3825 ✓…
Express 7429 as a product of its prime factors
Answer
Step 1: Check divisibility by small primes (2, 3, 5, 7, 11...) Step 2: 7429 is odd, so not divisible by 2 Step 3: Sum of digits: 7+4+2+9 = 22 (not divisible by 3) Step 4: Doesn't end in 0 or 5, so not…
Find HCF(26, 91) and LCM(26, 91) using prime factorization, then verify that HCF × LCM = 26 × 91
Answer
Step 1: Prime factorizations: 26 = 2 × 13 91 = 7 × 13 Step 2: Find HCF (smallest power of common factors): Common prime factor: 13 HCF(26, 91) = 13 Step 3: Find LCM (greatest power of all factors): …
Find HCF(510, 92) and LCM(510, 92) using prime factorization
Answer
Step 1: Prime factorizations: 510 = 2 × 3 × 5 × 17 92 = 2² × 23 Step 2: Find HCF (common factors with smallest power): Common prime factor: 2 HCF(510, 92) = 2 Step 3: Find LCM (all prime factors wit…
When do you use the formula HCF(a,b) × LCM(a,b) = a × b? Give an example
Answer
Use this formula to: 1. Find LCM if HCF is already known 2. Find HCF if LCM is already known 3. Verify your HCF and LCM calculations Example: Given HCF(306, 657) = 9, find LCM(306, 657) Using the fo…
Find HCF and LCM of 6, 72, and 120 using prime factorization
Answer
Step 1: Prime factorizations: 6 = 2 × 3 72 = 2³ × 3² 120 = 2³ × 3 × 5 Step 2: Find HCF (smallest power of common factors): Common prime factors: 2 and 3 Smallest powers: 2¹ and 3¹ HCF(6, 72, 120) = 2…
Can 4ⁿ ever end with the digit 0 for any natural number n? Explain using the Fundamental Theorem of Arithmetic
Answer
Solution: Step 1: If 4ⁿ ends with 0, then 4ⁿ must be divisible by 10 Step 2: For divisibility by 10, the number must be divisible by both 2 and 5 Step 3: Prime factorization of 4ⁿ: 4ⁿ = (2²)ⁿ = 2²ⁿ S…
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