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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. All factors must be prime
Explanation: Step 1: In prime factorisation, a number is written as a product of prime numbers. Step 2: If any composite factor remains, the form is not final. Step 3: In exams, write only prime bases and their powers in the final answer.
Correct answer: A. (2^3\times3^2\times7)
Explanation: Step 1: Write (504=8\times63). Step 2: (8=2^3) and (63=3^2\times7), so (504=2^3\times3^2\times7). Step 3: Do not leave composite forms like 8 and 63 in the final answer.
Correct answer: A. (2^4\times3\times11)
Explanation: Step 1: (528) can be written as (16\times33). Step 2: (16=2^4) and (33=3\times11), so (528=2^4\times3\times11). Step 3: Since 33 is composite, split it into 3 and 11.
Correct answer: A. (2^4\times5\times7)
Explanation: Step 1: Write (560=16\times35). Step 2: (16=2^4) and (35=5\times7), so (560=2^4\times5\times7). Step 3: Since 35 is composite, write 5 and 7 in the final form.
Correct answer: A. (2\times3^2\times5\times7)
Explanation: Step 1: Write (630=63\times10). Step 2: (63=3^2\times7) and (10=2\times5), so (630=2\times3^2\times5\times7). Step 3: Do not keep 9 or 35 in the final form.
Correct answer: A. (2^5\times3\times7)
Explanation: Step 1: (672) can be written as (32\times21). Step 2: (32=2^5) and (21=3\times7), so (672=2^5\times3\times7). Step 3: Since 21 is composite, break it further.
Correct answer: A. (2^2\times5^2\times7)
Explanation: Step 1: Write (700=7\times100). Step 2: (100=2^2\times5^2), so (700=2^2\times5^2\times7). Step 3: It is necessary to change 100 into prime powers.
Correct answer: A. (2^2\times3^3\times7)
Explanation: Step 1: Write (756=27\times28). Step 2: (27=3^3) and (28=2^2\times7), so (756=2^2\times3^3\times7). Step 3: Give complete prime form to both parts.
Correct answer: A. (3^3\times5\times7)
Explanation: Step 1: Write (945=27\times35). Step 2: (27=3^3) and (35=5\times7), so (945=3^3\times5\times7). Step 3: Do not forget to change 27 into (3^3).
Correct answer: A. (2^2\times5\times7^2)
Explanation: Step 1: Write (980=98\times10). Step 2: (98=2\times7^2) and (10=2\times5), so (980=2^2\times5\times7^2). Step 3: Count the total power of 2 correctly.
Correct answer: A. (2^4\times3^2\times7)
Explanation: Step 1: Write (1008=16\times63). Step 2: (16=2^4) and (63=3^2\times7), so (1008=2^4\times3^2\times7). Step 3: Give 63 its complete prime form.
Correct answer: A. (3\times5\times7\times11)
Explanation: Step 1: Write (1155=11\times105). Step 2: (105=3\times5\times7), so (1155=3\times5\times7\times11). Step 3: Since 105 is composite, break it further.
Correct answer: A. (2^3\times3\times7^2)
Explanation: Step 1: Write (1176=24\times49). Step 2: (24=2^3\times3) and (49=7^2), so (1176=2^3\times3\times7^2). Step 3: Convert 24 and 49 into prime powers.
Correct answer: A. (5^2\times7^2)
Explanation: Step 1: Recognise (1225=35^2). Step 2: Since (35=5\times7), (1225=5^2\times7^2). Step 3: In a square number, prime exponents may be even.
Correct answer: A. (2^4\times3^4)
Explanation: Step 1: Write (1296=16\times81). Step 2: (16=2^4) and (81=3^4), so (1296=2^4\times3^4). Step 3: Do not leave 16 and 81 in the final answer.
Correct answer: A. (3^3\times7^2)
Explanation: Step 1: Write (1323=27\times49). Step 2: (27=3^3) and (49=7^2), so (1323=3^3\times7^2). Step 3: Both 27 and 49 are composite, so write them as prime powers.
Correct answer: A. (2^5\times3^2\times5)
Explanation: Step 1: Write (1440=144\times10). Step 2: (144=2^4\times3^2) and (10=2\times5), so (1440=2^5\times3^2\times5). Step 3: The total power of 2 is 5.
Correct answer: A. (2\times3\times5\times7^2)
Explanation: Step 1: Write (1470=30\times49). Step 2: (30=2\times3\times5) and (49=7^2), so (1470=2\times3\times5\times7^2). Step 3: Write 49 as (7^2).
Correct answer: A. (2^6\times3^3)
Explanation: Step 1: Recognise (1728=12^3). Step 2: Since (12=2^2\times3), (12^3=2^6\times3^3). Step 3: Since 12 is composite, write powers of 2 and 3 in the final form.
Correct answer: A. (2^3\times3^2\times5^2)
Explanation: Step 1: Write (1800=18\times100). Step 2: (18=2\times3^2) and (100=2^2\times5^2), so (1800=2^3\times3^2\times5^2). Step 3: Give complete prime form to both 18 and 100.
Correct answer: A. (2^2\times3^2\times5\times11)
Explanation: Step 1: Write (1980=198\times10). Step 2: (198=2\times3^2\times11) and (10=2\times5), so (1980=2^2\times3^2\times5\times11). Step 3: Since 2 appears twice, write (2^2).
Correct answer: A. 3
Explanation: Step 1: (840=84\times10). Step 2: (84=2^2\times3\times7) and (10=2\times5), so (840=2^3\times3\times5\times7). Step 3: Comparing gives (a=3).
Correct answer: A. 3
Explanation: Step 1: (945=27\times35). Step 2: (27=3^3) and (35=5\times7), so (945=3^3\times5\times7). Step 3: Comparing gives (b=3).
Correct answer: A. 2
Explanation: Step 1: (1225=35^2). Step 2: Since (35=5\times7), (1225=5^2\times7^2). Step 3: Comparing with the given form gives (m=2).
Correct answer: A. 3
Explanation: Step 1: Write (1800=18\times100). Step 2: (18=2\times3^2) and (100=2^2\times5^2), so the total power of 2 is 3. Step 3: Therefore, (p=3).
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