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SubjectsMathematics
अभाज्य गुणनखंडन
In Class 10 Mathematics, under the Real Numbers chapter, Prime Factorisation teaches students to express a composite number as a product of prime numbers. Students practise identifying prime factors and writing factorisations using multiplication and exponents. This foundational skill supports the Fundamental Theorem of Arithmetic and later work with HCF and LCM.
TOPIC PRACTICE
Up to 10 questions from this page. Select your focus, then start.
Step 1: The bases of the first number are (2,3,5). Step 2: The bases of the second number are (2,3,7), so the common primes are (2) and (3). Step 3: For common factors, choose bases present in both numbers.
View question detailsStep 1: In HCF, take the smaller exponent of a common prime. Step 2: The exponents of (3) are (2) and (4), so the smaller exponent is (2). Step 3: For HCF, remember the minimum exponent rule.
View question detailsStep 1: In LCM, take the larger exponent of each prime. Step 2: The exponents of (2) are (5) and (3), so the larger exponent is (5). Step 3: For LCM, choose the maximum exponent.
View question detailsStep 1: Write (343) as (7 \times 49). Step 2: Since (49=7^2), (343=7^3). Step 3: (49 \times 7) gives the value, but it is not final prime factorisation.
View question detailsStep 1: An even factor must have exponent of (2) at least (1). Step 2: (2) has (3) choices (1,2,3), (3) has (3) choices (0,1,2), and (5) has (2) choices (0,1). Total (18). Step 3: While counting even factors, do not take exponent (0) for (2).
View question detailsStep 1: In an odd factor, the exponent of (2) must be (0). Step 2: The exponent of (3) can be (0,1,2,3), giving (4) odd factors. Step 3: While counting odd factors, remove (2) completely.
View question detailsStep 1: Trailing zeros are formed by pairs of (2) and (5). Step 2: The number of pairs equals the smaller of (a) and (b). So (\min(a,b)=5). Step 3: For trailing zeros, use the smaller exponent, not the sum.
View question detailsStep 1: A prime number has exactly two positive factors. Step 2: (1) has only one positive factor, so it is not prime and has no prime factor. Step 3: Avoid the common mistake of treating (1) as prime.
View question detailsStep 1: Every integer greater than (1) can be written as a product of prime factors. Step 2: This form is unique apart from order, and this comes from the fundamental theorem of arithmetic. Step 3: Remember uniqueness of prime factorisation with this theorem.
View question detailsStep 1: Write (432) as (16 \times 27). Step 2: (16=2^4) and (27=3^3), so (432=2^4 \times 3^3). Hence (a=4, b=3). Step 3: For unknown exponents, split the number into familiar powers.
View question detailsQUIZ COMPLETE
