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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 final form of prime factorisation is based only on prime numbers. Step 2: If a base like (45) remains, it must be written as (45=3^2\times5). Step 3: In exams, check every base before writing the final answer.
Correct answer: A. (2^4\times3^4\times11)
Explanation: Step 1: Write (14256=16\times891). Step 2: (16=2^4) and (891=3^4\times11), so (14256=2^4\times3^4\times11). Step 3: Do not leave 891 in the final form.
Correct answer: A. (2^5\times3^4\times7)
Explanation: Step 1: Write (18144=32\times567). Step 2: (32=2^5) and (567=3^4\times7), so (18144=2^5\times3^4\times7). Step 3: Give 567 its complete prime form.
Correct answer: A. (2^3\times5^2\times11^2)
Explanation: Step 1: Write (24200=200\times121). Step 2: (200=2^3\times5^2) and (121=11^2), so (24200=2^3\times5^2\times11^2). Step 3: Do not leave 200 and 121 in the final form.
Correct answer: A. (2\times3\times5\times7\times11^2)
Explanation: Step 1: Write (25410=210\times121). Step 2: (210=2\times3\times5\times7) and (121=11^2), so (25410=2\times3\times5\times7\times11^2). Step 3: Give prime form to both 210 and 121.
Correct answer: A. (2^4\times3^5\times7)
Explanation: Step 1: Write (27216=16\times1701). Step 2: (1701=3^5\times7), so (27216=2^4\times3^5\times7). Step 3: Convert 1701 into prime form using 3 and 7.
Correct answer: A. (2^5\times3^3\times5\times7)
Explanation: Step 1: Write (30240=32\times945). Step 2: (945=3^3\times5\times7), so (30240=2^5\times3^3\times5\times7). Step 3: Do not keep 945 in the final answer.
Correct answer: A. (2^2\times3\times5^2\times11^2)
Explanation: Step 1: Write (36300=300\times121). Step 2: (300=2^2\times3\times5^2) and (121=11^2), so (36300=2^2\times3\times5^2\times11^2). Step 3: Convert 300 and 121 into prime powers.
Correct answer: A. (3^2\times5\times7\times11^2)
Explanation: Step 1: Write (38115=315\times121). Step 2: (315=3^2\times5\times7) and (121=11^2), so (38115=3^2\times5\times7\times11^2). Step 3: Break both parts completely.
Correct answer: A. (2^6\times3^3\times5^2)
Explanation: Step 1: Write (43200=432\times100). Step 2: (432=2^4\times3^3) and (100=2^2\times5^2), so (43200=2^6\times3^3\times5^2). Step 3: Count the total power of 2 as 6.
Correct answer: A. (2\times3^2\times5\times7^2\times11)
Explanation: Step 1: Write (48510=90\times539). Step 2: (90=2\times3^2\times5) and (539=7^2\times11), so (48510=2\times3^2\times5\times7^2\times11). Step 3: Give prime form to both 90 and 539.
Correct answer: A. (2^3\times3^3\times5\times7^2)
Explanation: Step 1: Write (52920=8\times6615). Step 2: (6615=3^3\times5\times7^2), so (52920=2^3\times3^3\times5\times7^2). Step 3: Give 6615 its complete prime form.
Correct answer: A. (2\times5\times7\times11^3)
Explanation: Step 1: Write (59290=70\times1331). Step 2: (70=2\times5\times7) and (1331=11^3), so (59290=2\times5\times7\times11^3). Step 3: Change 1331 into (11^3).
Correct answer: A. (2^{16})
Explanation: Step 1: Divide 65536 repeatedly by 2. Step 2: Sixteen factors of 2 give (65536=2^{16}). Step 3: 256 and 16 are composite bases, so write the power of 2 in final form.
Correct answer: A. (2^3\times3^5\times5\times7)
Explanation: Step 1: Write (68040=8\times8505). Step 2: (8505=3^5\times5\times7), so (68040=2^3\times3^5\times5\times7). Step 3: Convert 8505 into prime powers.
Correct answer: A. (2\times3^2\times5\times7\times11^2)
Explanation: Step 1: Write (76230=630\times121). Step 2: (630=2\times3^2\times5\times7) and (121=11^2), so (76230=2\times3^2\times5\times7\times11^2). Step 3: Break both 630 and 121 completely.
Correct answer: A. (2^3\times3^2\times5^2\times7^2)
Explanation: Step 1: Write (88200=8\times11025). Step 2: (11025=3^2\times5^2\times7^2), so (88200=2^3\times3^2\times5^2\times7^2). Step 3: Convert 11025 into prime powers.
Correct answer: A. (2^3\times3^5\times7^2)
Explanation: Step 1: Write (95256=8\times11907). Step 2: (11907=3^5\times7^2), so (95256=2^3\times3^5\times7^2). Step 3: Convert 11907 into powers of 3 and 7.
Correct answer: A. (2^2\times3^2\times5^2\times11^2)
Explanation: Step 1: Write (108900=900\times121). Step 2: (900=2^2\times3^2\times5^2) and (121=11^2), so (108900=2^2\times3^2\times5^2\times11^2). Step 3: This is a square form, so all exponents are even.
Correct answer: A. (2^5\times3^4\times7^2)
Explanation: Step 1: Write (127008=32\times3969). Step 2: (3969=3^4\times7^2), so (127008=2^5\times3^4\times7^2). Step 3: Convert 3969 into prime powers.
Correct answer: A. (2^3\times3^3\times5\times11^2)
Explanation: Step 1: Write (130680=1080\times121). Step 2: (1080=2^3\times3^3\times5) and (121=11^2), so (130680=2^3\times3^3\times5\times11^2). Step 3: Break 1080 and 121 completely.
Correct answer: A. 5
Explanation: Step 1: (127008=32\times3969). Step 2: (32=2^5) and (3969=3^4\times7^2), so the power of 2 is 5. Step 3: Comparing gives (a=5).
Correct answer: A. 5
Explanation: Step 1: Write (95256=8\times11907). Step 2: (11907=3^5\times7^2), so (95256=2^3\times3^5\times7^2). Step 3: From the given form, (b=5).
Correct answer: A. 2
Explanation: Step 1: (108900=900\times121). Step 2: (900=2^2\times3^2\times5^2) and (121=11^2), so the power of 5 is 2. Step 3: Comparing gives (m=2).
Correct answer: A. 5
Explanation: Step 1: Write (68040=8\times8505). Step 2: (8505=3^5\times5\times7), so the power of 3 is 5. Step 3: Comparing gives (p=5).
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