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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 only prime bases should remain in the final form
Explanation: Step 1: The aim of prime factorisation is to write the number using prime bases only. Step 2: If a base like (45) or (121) remains, it is composite and must be broken further. Step 3: Before writing the final answer, check whether every base is prime.
Correct answer: A. (2^4\times3^5\times5^2\times7)
Explanation: Step 1: Write (680400=16\times42525). Step 2: (16=2^4) and (42525=3^5\times5^2\times7), so the correct form is (2^4\times3^5\times5^2\times7). Step 3: Do not leave 42525 in the final form.
Correct answer: A. (2^6\times3^4\times11^2)
Explanation: Step 1: Write (627264=64\times9801). Step 2: (64=2^6) and (9801=3^4\times11^2), so (627264=2^6\times3^4\times11^2). Step 3: Convert 9801 into prime powers.
Correct answer: A. (2^3\times3^6\times5\times13)
Explanation: Step 1: Write (379080=8\times47385). Step 2: (8=2^3) and (47385=3^6\times5\times13), so the correct form is (2^3\times3^6\times5\times13). Step 3: Give 47385 its complete prime form.
Correct answer: A. (2^5\times5^3\times7^2)
Explanation: Step 1: Write (196000=32\times6125). Step 2: (32=2^5) and (6125=5^3\times7^2), so (196000=2^5\times5^3\times7^2). Step 3: Do not keep 6125 in the final answer.
Correct answer: A. (3^4\times5^2\times11\times13)
Explanation: Step 1: Write (289575=81\times3575). Step 2: (81=3^4) and (3575=5^2\times11\times13), so (289575=3^4\times5^2\times11\times13). Step 3: Give 3575 its complete prime form too.
Correct answer: A. (2^8\times3^2\times7\times11)
Explanation: Step 1: Write (177408=256\times693). Step 2: (256=2^8) and (693=3^2\times7\times11), so the correct form is (2^8\times3^2\times7\times11). Step 3: Convert 693 into prime form.
Correct answer: A. (2^4\times3^3\times5^2\times7^2)
Explanation: Step 1: Write (529200=16\times33075). Step 2: (33075=3^3\times5^2\times7^2), so (529200=2^4\times3^3\times5^2\times7^2). Step 3: Do not leave 33075 in the final form.
Correct answer: A. (2^7\times3^5\times5)
Explanation: Step 1: Write (155520=128\times1215). Step 2: (128=2^7) and (1215=3^5\times5), so (155520=2^7\times3^5\times5). Step 3: Convert 1215 into prime powers.
Correct answer: A. (2^2\times3^4\times7^2\times11)
Explanation: Step 1: Write (174636=4\times43659). Step 2: (4=2^2) and (43659=3^4\times7^2\times11), so the correct form is (2^2\times3^4\times7^2\times11). Step 3: Convert 43659 into prime powers.
Correct answer: A. (2^5\times3^2\times5^2\times11)
Explanation: Step 1: Write (79200=32\times2475). Step 2: (2475=3^2\times5^2\times11), so (79200=2^5\times3^2\times5^2\times11). Step 3: Give 2475 its complete prime form.
Correct answer: A. (2^3\times3^3\times5^2\times7\times11)
Explanation: Step 1: Write (415800=8\times51975). Step 2: (51975=3^3\times5^2\times7\times11), so (415800=2^3\times3^3\times5^2\times7\times11). Step 3: Do not leave 51975 in the final form.
Correct answer: A. (2^6\times3^5\times7^2)
Explanation: Step 1: Write (762048=64\times11907). Step 2: (64=2^6) and (11907=3^5\times7^2), so (762048=2^6\times3^5\times7^2). Step 3: Write 11907 as prime powers.
Correct answer: A. (2^4\times5^2\times7^3)
Explanation: Step 1: Write (137200=16\times8575). Step 2: (16=2^4) and (8575=5^2\times7^3), so the correct form is (2^4\times5^2\times7^3). Step 3: Give 8575 its final prime form.
Correct answer: A. (3^6\times5^2\times7)
Explanation: Step 1: Write (127575=729\times175). Step 2: (729=3^6) and (175=5^2\times7), so (127575=3^6\times5^2\times7). Step 3: Give prime form to both 729 and 175.
Correct answer: A. (2^5\times3^4\times5^2\times7)
Explanation: Step 1: Write (453600=32\times14175). Step 2: (14175=3^4\times5^2\times7), so (453600=2^5\times3^4\times5^2\times7). Step 3: Do not leave 14175 in the final form.
Correct answer: A. (2^7\times3^2\times11^2)
Explanation: Step 1: Write (139392=128\times1089). Step 2: (128=2^7) and (1089=3^2\times11^2), so (139392=2^7\times3^2\times11^2). Step 3: Convert 1089 into prime powers.
Correct answer: A. (2^3\times3^2\times5^3\times13)
Explanation: Step 1: Write (117000=8\times14625). Step 2: (14625=3^2\times5^3\times13), so (117000=2^3\times3^2\times5^3\times13). Step 3: Give 14625 its complete prime form.
Correct answer: A. (2^6\times3^3\times5^2\times11)
Explanation: Step 1: Write (475200=64\times7425). Step 2: (7425=3^3\times5^2\times11), so (475200=2^6\times3^3\times5^2\times11). Step 3: Do not leave 7425 in the final form.
Correct answer: A. (3^4\times5^2\times7^2)
Explanation: Step 1: Write (99225=81\times1225). Step 2: (81=3^4) and (1225=5^2\times7^2), so (99225=3^4\times5^2\times7^2). Step 3: Convert 1225 into prime powers.
Correct answer: A. (2^8\times3^4\times5^2)
Explanation: Step 1: Write (518400=256\times2025). Step 2: (256=2^8) and (2025=3^4\times5^2), so (518400=2^8\times3^4\times5^2). Step 3: Give 2025 its final prime form.
Correct answer: A. 2
Explanation: Step 1: (529200=16\times33075). Step 2: (33075=3^3\times5^2\times7^2), so the power of 7 is 2. Step 3: Comparing gives (q=2).
Correct answer: A. 6
Explanation: Step 1: Write (627264=64\times9801). Step 2: (64=2^6) and (9801=3^4\times11^2), so the power of 2 is 6. Step 3: From the given form, (a=6).
Correct answer: A. 5
Explanation: Step 1: (680400=16\times42525). Step 2: (42525=3^5\times5^2\times7), so the power of 3 is 5. Step 3: Comparing gives (b=5).
Correct answer: A. 3
Explanation: Step 1: Write (137200=16\times8575). Step 2: (8575=5^2\times7^3), so the power of 7 is 3. Step 3: From the given form, (p=3).
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