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SubjectsMathematics
अभाज्य गुणनखंडन द्वारा महत्तम समापवर्तक और लघुत्तम समापवर्त्य
In this Class 10 Mathematics topic from Real Numbers, students learn to find the HCF and LCM of two or more numbers through prime factorisation. They break each number into prime factors, compare the resulting powers, and select the appropriate common factors: the lowest powers for HCF and the highest powers for LCM. The topic also develops accuracy in writing factor trees, simplifies comparison between methods, and helps students apply these concepts to numerical and everyday problem-solving situations.
TOPIC PRACTICE
Up to 4 questions from this page. Select your focus, then start.
Step 1: Subtract (16) from each number to get (720), (1120), and (1520). Step 2: The HCF of these three numbers is (80), so the greatest number is (80). Step 3: In fixed-remainder questions, subtract the remainder first and then find the HCF.
View question detailsStep 1: Product of two numbers equals HCF times LCM. Step 2: The other number is (\frac{54\times4158}{378}=594). Step 3: Notice (378=54\times7) and simplify the division first.
View question detailsStep 1: In each case, divisor minus remainder is (9), so adding (9) to the number makes it exactly divisible by all three divisors. Step 2: The LCM of (72), (90), and (126) is (2520), so the number is (2520-9=2511). Step 3: When each remainder is equally less than the divisor, subtract that common difference from the LCM.
View question detailsUse prime factorisation to find the highest common factor. We have 24 = 2³ × 3 and 36 = 2² × 3². The common primes are 2 and 3; taking the smaller exponent of each gives HCF = 2² × 3 = 4 × 3 = 12. Although 6 divides both numbers, 12 is the greatest common factor.
View question detailsQUIZ COMPLETE
