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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\times3^5)
Explanation: Step 1: Write (486=2\times243). Step 2: Since (243=3^5), (486=2\times3^5). Step 3: Do not leave 243 in the final answer; write it as a power of 3.
Correct answer: A. (2^3\times3\times5^2)
Explanation: Step 1: Write (600=6\times100). Step 2: (6=2\times3) and (100=2^2\times5^2), so (600=2^3\times3\times5^2). Step 3: Be careful while counting the total power of 2.
Correct answer: A. (3^3\times5^2)
Explanation: Step 1: Write (675=27\times25). Step 2: (27=3^3) and (25=5^2), so (675=3^3\times5^2). Step 3: 27 and 25 are composite, so convert them into prime powers.
Correct answer: A. (2^4\times3^2\times5)
Explanation: Step 1: Write (720=72\times10). Step 2: (72=2^3\times3^2) and (10=2\times5), so (720=2^4\times3^2\times5). Step 3: Break 72 completely into prime form.
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: Convert 28 into (2^2\times7).
Correct answer: A. (2^4\times7^2)
Explanation: Step 1: Recognise (784=28^2). Step 2: Since (28=2^2\times7), (784=2^4\times7^2). Step 3: In a square number, exponents may be even, so check the powers.
Correct answer: A. (2^3\times3\times5\times7)
Explanation: Step 1: Write (840=84\times10). Step 2: (84=2^2\times3\times7) and (10=2\times5), so (840=2^3\times3\times5\times7). Step 3: Break all composite factors down to primes.
Correct answer: A. (2^2\times3^2\times5^2)
Explanation: Step 1: Write (900=9\times100). Step 2: (9=3^2) and (100=2^2\times5^2), so (900=2^2\times3^2\times5^2). Step 3: 900 is a square number, so even exponents appear.
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. (2^3\times5^3)
Explanation: Step 1: (1000) can be written as (10^3). Step 2: Since (10=2\times5), (1000=2^3\times5^3). Step 3: 10 is composite, so write 2 and 5 in the final prime form.
Correct answer: A. (2^{10})
Explanation: Step 1: Divide 1024 repeatedly by 2. Step 2: Ten factors of 2 give (1024=2^{10}). Step 3: 4 and 32 are composite, so write the power of 2 in final 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: 105 is composite, so 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: Write both 24 and 49 in prime form.
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: 35 is composite, so write prime bases 5 and 7.
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: Convert 16 and 81 into prime powers.
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: Do not leave 27 and 49 in the final form.
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, so count it carefully.
Correct answer: A. (3^2\times5^2\times7)
Explanation: Step 1: Write (1575=225\times7). Step 2: (225=3^2\times5^2), so (1575=3^2\times5^2\times7). Step 3: Convert 225 into prime powers.
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: 12 is composite, so write powers of 2 and 3 in the final prime form.
Correct answer: A. (2^2\times3^2\times7^2)
Explanation: Step 1: (1764=42^2). Step 2: Since (42=2\times3\times7), (1764=2^2\times3^2\times7^2). Step 3: In a square number, each prime power should be even.
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: Break 18 and 100 separately into prime form.
Correct answer: A. (3^4\times5^2)
Explanation: Step 1: Write (2025=81\times25). Step 2: (81=3^4) and (25=5^2), so (2025=3^4\times5^2). Step 3: Convert 81 and 25 into prime powers.
Correct answer: A. (3^7)
Explanation: Step 1: Divide 2187 repeatedly by 3. Step 2: Seven factors of 3 give (2187=3^7). Step 3: 9 and 27 are composite, so keep base 3 in the final form.
Correct answer: A. (7^4)
Explanation: Step 1: (2401) can be written as (49\times49). Step 2: Since (49=7^2), (2401=7^4). Step 3: 49 is composite, so write the power of 7 in final prime form.
Correct answer: A. (2^2\times5^4)
Explanation: Step 1: Write (2500=25\times100). Step 2: (25=5^2) and (100=2^2\times5^2), so (2500=2^2\times5^4). Step 3: The total power of 5 is 4, so count carefully.
