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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. Because 36 is composite
Explanation: Step 1: In final prime factorisation, the bases should be prime. Step 2: (36=2^2\times3^2), so (36^2) must be changed into (2^4\times3^4). Step 3: Do not keep a composite base like 36 in the final answer.
Correct answer: A. (2^3\times3^2\times7\times11)
Explanation: Step 1: Write (5544=8\times693). Step 2: (8=2^3) and (693=3^2\times7\times11), so (5544=2^3\times3^2\times7\times11). Step 3: Do not leave 693 in the final form.
Correct answer: A. (2^5\times3^3\times7)
Explanation: Step 1: Write (6048=32\times189). Step 2: (32=2^5) and (189=3^3\times7), so (6048=2^5\times3^3\times7). Step 3: Change 189 into (3^3\times7).
Correct answer: A. (2\times3^2\times5\times7\times11)
Explanation: Step 1: Write (6930=63\times110). Step 2: (63=3^2\times7) and (110=2\times5\times11), so (6930=2\times3^2\times5\times7\times11). Step 3: Give prime form to both 63 and 110.
Correct answer: A. (2^2\times3^3\times7\times11)
Explanation: Step 1: Write (8316=36\times231). Step 2: (36=2^2\times3^2) and (231=3\times7\times11), so (8316=2^2\times3^3\times7\times11). Step 3: The total power of 3 becomes 3.
Correct answer: A. (2^3\times3\times5\times7\times11)
Explanation: Step 1: Write (9240=8\times1155). Step 2: (8=2^3) and (1155=3\times5\times7\times11), so (9240=2^3\times3\times5\times7\times11). Step 3: Give 1155 its complete prime form.
Correct answer: A. (3^3\times5\times7\times11)
Explanation: Step 1: Write (10395=27\times385). Step 2: (27=3^3) and (385=5\times7\times11), so (10395=3^3\times5\times7\times11). Step 3: Break 385 into prime form too.
Correct answer: A. (3^2\times5^2\times7^2)
Explanation: Step 1: Recognise (11025=105^2). Step 2: Since (105=3\times5\times7), (11025=3^2\times5^2\times7^2). Step 3: In a square number, prime exponents are even.
Correct answer: A. (2^4\times3\times5\times7^2)
Explanation: Step 1: Write (11760=16\times735). Step 2: (16=2^4) and (735=3\times5\times7^2), so (11760=2^4\times3\times5\times7^2). Step 3: Give 735 its complete prime form.
Correct answer: A. (2^5\times3^2\times7^2)
Explanation: Step 1: Write (14112=32\times441). Step 2: (32=2^5) and (441=3^2\times7^2), so (14112=2^5\times3^2\times7^2). Step 3: Change 441 into (3^2\times7^2).
Correct answer: A. (2^4\times3^3\times5\times7)
Explanation: Step 1: Write (15120=16\times945). Step 2: (16=2^4) and (945=3^3\times5\times7), so (15120=2^4\times3^3\times5\times7). Step 3: Do not leave 945 in the final form.
Correct answer: A. (2^3\times3^3\times7\times11)
Explanation: Step 1: Write (16632=8\times2079). Step 2: (2079=3^3\times7\times11), so (16632=2^3\times3^3\times7\times11). Step 3: Break 2079 down to prime factors.
Correct answer: A. (2^3\times3^2\times5\times7^2)
Explanation: Step 1: Write (17640=8\times2205). Step 2: (2205=3^2\times5\times7^2), so (17640=2^3\times3^2\times5\times7^2). Step 3: Give 2205 its complete prime form.
Correct answer: A. (2^4\times5^2\times7^2)
Explanation: Step 1: Recognise (19600=140^2). Step 2: Since (140=2^2\times5\times7), (19600=2^4\times5^2\times7^2). Step 3: Check evenness of exponents in square numbers.
Correct answer: A. (2\times3^3\times5\times7\times11)
Explanation: Step 1: Write (20790=54\times385). Step 2: (54=2\times3^3) and (385=5\times7\times11), so (20790=2\times3^3\times5\times7\times11). Step 3: Break both 54 and 385 completely.
Correct answer: A. (2^4\times3^3\times7^2)
Explanation: Step 1: Write (21168=16\times1323). Step 2: (1323=3^3\times7^2), so (21168=2^4\times3^3\times7^2). Step 3: Convert 1323 into powers of 3 and 7.
Correct answer: A. (3^2\times5\times7^2\times11)
Explanation: Step 1: Write (24255=45\times539). Step 2: (45=3^2\times5) and (539=7^2\times11), so (24255=3^2\times5\times7^2\times11). Step 3: Give 539 its prime form too.
Correct answer: A. (2^3\times3^2\times5\times7\times11)
Explanation: Step 1: Write (27720=8\times3465). Step 2: (3465=3^2\times5\times7\times11), so (27720=2^3\times3^2\times5\times7\times11). Step 3: Break 3465 completely.
Correct answer: A. (2^6\times3^2\times7^2)
Explanation: Step 1: Write (28224=64\times441). Step 2: (64=2^6) and (441=3^2\times7^2), so (28224=2^6\times3^2\times7^2). Step 3: Write 441 as prime powers.
Correct answer: A. (2^7\times3^5)
Explanation: Step 1: Write (31104=128\times243). Step 2: (128=2^7) and (243=3^5), so (31104=2^7\times3^5). Step 3: 128 and 243 are composite, so keep prime bases.
Correct answer: A. (2^4\times3^2\times5\times7^2)
Explanation: Step 1: Write (35280=16\times2205). Step 2: (2205=3^2\times5\times7^2), so (35280=2^4\times3^2\times5\times7^2). Step 3: Give 2205 its complete prime form.
Correct answer: A. 3
Explanation: Step 1: (27720=8\times3465). Step 2: (8=2^3) and (3465=3^2\times5\times7\times11), so the power of 2 is 3. Step 3: Comparing gives (a=3).
Correct answer: A. 5
Explanation: Step 1: Write (31104=128\times243). Step 2: (128=2^7) and (243=3^5), so (31104=2^7\times3^5). Step 3: Comparing with the given form gives (b=5).
Correct answer: A. 2
Explanation: Step 1: (19600=140^2). Step 2: (140=2^2\times5\times7), so (19600=2^4\times5^2\times7^2). Step 3: Comparing gives (m=2).
Correct answer: A. 3
Explanation: Step 1: Write (20790=54\times385). Step 2: (54=2\times3^3) and (385=5\times7\times11), so the power of 3 is 3. Step 3: Comparing gives (p=3).
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