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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.
Correct answer: A. The factorisation is not considered complete
Explanation: Step 1: In final prime factorisation, every base must be prime. Step 2: If a composite base like 12 or 21 remains, it must be broken further. Step 3: In exams, check every base before writing the final form.
Correct answer: A. (2^3\times3^2\times11)
Explanation: Step 1: Write (792=8\times99). Step 2: (8=2^3) and (99=3^2\times11), so (792=2^3\times3^2\times11). Step 3: Do not leave 99 in the final answer.
Correct answer: A. (3\times5^2\times11)
Explanation: Step 1: Write (825=25\times33). Step 2: (25=5^2) and (33=3\times11), so (825=3\times5^2\times11). Step 3: Both 25 and 33 are composite, so convert them into prime form.
Correct answer: A. (2^5\times3^3)
Explanation: Step 1: Write (864=32\times27). Step 2: (32=2^5) and (27=3^3), so (864=2^5\times3^3). Step 3: It is necessary to convert 32 and 27 into prime powers.
Correct answer: A. (2^2\times3\times7\times11)
Explanation: Step 1: Write (924=4\times231). Step 2: (4=2^2) and (231=3\times7\times11), so (924=2^2\times3\times7\times11). Step 3: Give 231 its complete prime form.
Correct answer: A. (2\times3\times5^2\times7)
Explanation: Step 1: Write (1050=105\times10). Step 2: (105=3\times5\times7) and (10=2\times5), so (1050=2\times3\times5^2\times7). Step 3: Since 5 appears twice, write (5^2).
Correct answer: A. (2^2\times3^3\times11)
Explanation: Step 1: Write (1188=4\times297). Step 2: (4=2^2) and (297=3^3\times11), so (1188=2^2\times3^3\times11). Step 3: Break 297 into 3 and 11 form.
Correct answer: A. (2^2\times3^2\times5\times7)
Explanation: Step 1: Write (1260=126\times10). Step 2: (126=2\times3^2\times7) and (10=2\times5), so (1260=2^2\times3^2\times5\times7). Step 3: The total power of 2 is 2.
Correct answer: A. (2\times3^3\times5^2)
Explanation: Step 1: Write (1350=27\times50). Step 2: (27=3^3) and (50=2\times5^2), so (1350=2\times3^3\times5^2). Step 3: Do not leave 27 and 50 in the final form.
Correct answer: A. (2\times3^2\times7\times11)
Explanation: Step 1: Write (1386=18\times77). Step 2: (18=2\times3^2) and (77=7\times11), so (1386=2\times3^2\times7\times11). Step 3: Give prime form to both 18 and 77.
Correct answer: A. (2^2\times3\times5^3)
Explanation: Step 1: Write (1500=15\times100). Step 2: (15=3\times5) and (100=2^2\times5^2), so (1500=2^2\times3\times5^3). Step 3: Count the total power of 5 as 3.
Correct answer: A. (2^4\times3^2\times11)
Explanation: Step 1: Write (1584=16\times99). Step 2: (16=2^4) and (99=3^2\times11), so (1584=2^4\times3^2\times11). Step 3: Do not leave 99 in the final form.
Correct answer: A. (2^4\times3\times5\times7)
Explanation: Step 1: Write (1680=16\times105). Step 2: (16=2^4) and (105=3\times5\times7), so (1680=2^4\times3\times5\times7). Step 3: Change 105 into prime factors.
Correct answer: A. (2\times3^3\times5\times7)
Explanation: Step 1: Write (1890=27\times70). Step 2: (27=3^3) and (70=2\times5\times7), so (1890=2\times3^3\times5\times7). Step 3: Change 27 into (3^3).
Correct answer: A. (2^2\times3\times5^2\times7)
Explanation: Step 1: Write (2100=21\times100). Step 2: (21=3\times7) and (100=2^2\times5^2), so (2100=2^2\times3\times5^2\times7). Step 3: Do not keep 25 or 100 in the final answer.
Correct answer: A. (2\times3\times5\times7\times11)
Explanation: Step 1: Write (2310=30\times77). Step 2: (30=2\times3\times5) and (77=7\times11), so (2310=2\times3\times5\times7\times11). Step 3: Break both 30 and 77 completely.
Correct answer: A. (2^3\times3^2\times5\times7)
Explanation: Step 1: Write (2520=252\times10). Step 2: (252=2^2\times3^2\times7) and (10=2\times5), so (2520=2^3\times3^2\times5\times7). Step 3: Count the total power of 2 correctly.
Correct answer: A. (2^2\times3^2\times7\times11)
Explanation: Step 1: Write (2772=36\times77). Step 2: (36=2^2\times3^2) and (77=7\times11), so (2772=2^2\times3^2\times7\times11). Step 3: Write 36 and 77 in prime form.
Correct answer: A. (2^4\times3^3\times7)
Explanation: Step 1: Write (3024=16\times189). Step 2: (16=2^4) and (189=3^3\times7), so (3024=2^4\times3^3\times7). Step 3: Give 189 its complete prime form.
Correct answer: A. (2\times3^2\times5^2\times7)
Explanation: Step 1: Write (3150=315\times10). Step 2: (315=3^2\times5\times7) and (10=2\times5), so (3150=2\times3^2\times5^2\times7). Step 3: The power of 5 becomes 2.
Correct answer: A. (2^5\times3\times5\times7)
Explanation: Step 1: Write (3360=32\times105). Step 2: (32=2^5) and (105=3\times5\times7), so (3360=2^5\times3\times5\times7). Step 3: Do not keep 105 in the final form.
Correct answer: A. 2
Explanation: Step 1: Write (1260=126\times10). Step 2: (126=2\times3^2\times7) and (10=2\times5), so the total power of 2 is 2. Step 3: Therefore, (a=2).
Correct answer: A. 3
Explanation: Step 1: (1350=27\times50). Step 2: (27=3^3) and (50=2\times5^2), so (1350=2\times3^3\times5^2). Step 3: Comparing gives (b=3).
Correct answer: A. 2
Explanation: Step 1: Write (1500=15\times100). Step 2: (15=3\times5) and (100=2^2\times5^2), so the power of 2 is 2. Step 3: Comparing gives (p=2).
Correct answer: A. 2
Explanation: Step 1: (2100=21\times100). Step 2: (21=3\times7) and (100=2^2\times5^2), so the power of 5 is 2. Step 3: Therefore, (q=2).
