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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. (2^2\times3\times11)
Explanation: Step 1: Write (132=4\times33). Step 2: (4=2^2) and (33=3\times11), so (132=2^2\times3\times11). Step 3: Do not keep composite factors like 4 and 33 in the final answer.
Correct answer: A. (2\times3\times5^2)
Explanation: Step 1: Write (150=15\times10). Step 2: (15=3\times5) and (10=2\times5), so (150=2\times3\times5^2). Step 3: When the same prime repeats, write it as a power.
Correct answer: A. (2\times3^4)
Explanation: Step 1: Write (162=2\times81). Step 2: Since (81=3^4), (162=2\times3^4). Step 3: Do not leave 81 in the final form; write (3^4).
Correct answer: A. (2^3\times3\times7)
Explanation: Step 1: Write (168=8\times21). Step 2: (8=2^3) and (21=3\times7), so (168=2^3\times3\times7). Step 3: 8 and 21 are composite, so break them further.
Correct answer: A. (2^2\times3^2\times5)
Explanation: Step 1: Write (180=18\times10). Step 2: (18=2\times3^2) and (10=2\times5), so (180=2^2\times3^2\times5). Step 3: Change all composite factors into prime form.
Correct answer: A. (2^2\times7^2)
Explanation: Step 1: (196) can be written as (14\times14) or (4\times49). Step 2: Since (14=2\times7), (196=2^2\times7^2). Step 3: In square numbers, exponents are often even, so check them.
Correct answer: A. (2\times3\times5\times7)
Explanation: Step 1: Write (210=21\times10). Step 2: (21=3\times7) and (10=2\times5), so (210=2\times3\times5\times7). Step 3: Do not keep 21 or 10 in the final answer.
Correct answer: A. (3^2\times5^2)
Explanation: Step 1: Recognise (225=15^2). Step 2: Since (15=3\times5), (225=3^2\times5^2). Step 3: 15 is composite, so write powers of 3 and 5 in the final form.
Correct answer: A. (3\times7\times11)
Explanation: Step 1: Write (231=21\times11). Step 2: Since (21=3\times7), (231=3\times7\times11). Step 3: 21 is composite, so do not keep it in the final answer.
Correct answer: A. (2^4\times3\times5)
Explanation: Step 1: Write (240=16\times15). Step 2: (16=2^4) and (15=3\times5), so (240=2^4\times3\times5). Step 3: It is necessary to change 16 into (2^4).
Correct answer: A. (2^2\times3^2\times7)
Explanation: Step 1: Write (252=4\times63). Step 2: (4=2^2) and (63=3^2\times7), so (252=2^2\times3^2\times7). Step 3: Break 63 completely into prime form too.
Correct answer: A. (2\times3^3\times5)
Explanation: Step 1: Write (270=27\times10). Step 2: (27=3^3) and (10=2\times5), so (270=2\times3^3\times5). Step 3: Do not forget to change 27 into (3^3).
Correct answer: A. (2\times3\times7^2)
Explanation: Step 1: Write (294=6\times49). Step 2: (6=2\times3) and (49=7^2), so (294=2\times3\times7^2). Step 3: Write 49 as (7^2).
Correct answer: A. (2^2\times3\times5^2)
Explanation: Step 1: Write (300=3\times100). Step 2: (100=2^2\times5^2), so (300=2^2\times3\times5^2). Step 3: Convert 100 into prime powers.
Correct answer: A. (3^2\times5\times7)
Explanation: Step 1: Write (315=9\times35). Step 2: (9=3^2) and (35=5\times7), so (315=3^2\times5\times7). Step 3: Change both 9 and 35 into prime form.
Correct answer: A. (2^2\times3^4)
Explanation: Step 1: Write (324=4\times81). Step 2: (4=2^2) and (81=3^4), so (324=2^2\times3^4). Step 3: Since it is a square number, check powers carefully.
Correct answer: A. (2\times3\times5\times11)
Explanation: Step 1: Write (330=33\times10). Step 2: (33=3\times11) and (10=2\times5), so (330=2\times3\times5\times11). Step 3: Break all composite factors further.
Correct answer: A. (7^3)
Explanation: Step 1: Write (343=7\times49). Step 2: Since (49=7^2), (343=7^3). Step 3: 49 is composite, so write (7^3) in the final form.
Correct answer: A. (2^3\times3^2\times5)
Explanation: Step 1: Write (360=36\times10). Step 2: (36=2^2\times3^2) and (10=2\times5), so (360=2^3\times3^2\times5). Step 3: Be careful while counting the total power of 2.
Correct answer: A. (3\times5^3)
Explanation: Step 1: Write (375=3\times125). Step 2: Since (125=5^3), (375=3\times5^3). Step 3: Change 125 into (5^3).
Correct answer: A. (2^3\times7^2)
Explanation: Step 1: Write (392=8\times49). Step 2: (8=2^3) and (49=7^2), so (392=2^3\times7^2). Step 3: Convert 8 and 49 into prime powers.
Correct answer: A. (2^4\times5^2)
Explanation: Step 1: Write (400=16\times25). Step 2: (16=2^4) and (25=5^2), so (400=2^4\times5^2). Step 3: Composite forms like 20 or 10 are not final answers.
Correct answer: A. (3^2\times7^2)
Explanation: Step 1: Recognise (441=21^2). Step 2: Since (21=3\times7), (441=3^2\times7^2). Step 3: 21 is composite, so write prime bases 3 and 7.
Correct answer: A. (2\times3^2\times5^2)
Explanation: Step 1: Write (450=45\times10). Step 2: (45=3^2\times5) and (10=2\times5), so (450=2\times3^2\times5^2). Step 3: Since 5 appears twice, write (5^2).
Correct answer: A. (2^5\times3\times5)
Explanation: Step 1: Write (480=48\times10). Step 2: (48=2^4\times3) and (10=2\times5), so (480=2^5\times3\times5). Step 3: Count the total power of 2 correctly.
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