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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 18 is composite
Explanation: Step 1: In the final prime factorisation, bases must be prime. Step 2: (18=2\times3^2), so (18^2) must be changed into (2^2\times3^4). Step 3: Do not leave a composite base in the final answer.
Correct answer: A. (2^3\times3^3\times11)
Explanation: Step 1: Write (2376=8\times297). Step 2: (8=2^3) and (297=3^3\times11), so (2376=2^3\times3^3\times11). Step 3: Do not leave 297 in the final form.
Correct answer: A. (3^2\times5\times7\times11)
Explanation: Step 1: Write (3465=9\times385). Step 2: (9=3^2) and (385=5\times7\times11), so (3465=3^2\times5\times7\times11). Step 3: Give 385 its complete prime form too.
Correct answer: A. (2\times3^2\times5\times7^2)
Explanation: Step 1: Write (4410=90\times49). Step 2: (90=2\times3^2\times5) and (49=7^2), so (4410=2\times3^2\times5\times7^2). Step 3: Give prime form to both 90 and 49.
Correct answer: A. (2^4\times3^2\times5\times7)
Explanation: Step 1: Write (5040=16\times315). Step 2: (16=2^4) and (315=3^2\times5\times7), so (5040=2^4\times3^2\times5\times7). Step 3: Give 315 its complete prime form.
Correct answer: A. (2^2\times3^3\times7^2)
Explanation: Step 1: Write (5292=4\times1323). Step 2: (4=2^2) and (1323=3^3\times7^2), so (5292=2^2\times3^3\times7^2). Step 3: Convert 1323 into powers of 3 and 7.
Correct answer: A. (2\times3^4\times5\times7)
Explanation: Step 1: Write (5670=81\times70). Step 2: (81=3^4) and (70=2\times5\times7), so (5670=2\times3^4\times5\times7). Step 3: It is necessary to change 81 into (3^4).
Correct answer: A. (2\times3\times5^2\times7^2)
Explanation: Step 1: Write (7350=150\times49). Step 2: (150=2\times3\times5^2) and (49=7^2), so (7350=2\times3\times5^2\times7^2). Step 3: Break 150 and 49 completely and separately.
Correct answer: A. (2^3\times3^3\times5\times7)
Explanation: Step 1: Write (7560=8\times945). Step 2: (8=2^3) and (945=3^3\times5\times7), so (7560=2^3\times3^3\times5\times7). Step 3: Do not leave 945 in the final form.
Correct answer: A. (3\times5\times7^2\times11)
Explanation: Step 1: Write (8085=15\times539). Step 2: (15=3\times5) and (539=7^2\times11), so (8085=3\times5\times7^2\times11). Step 3: Give 539 its complete prime form too.
Correct answer: A. (2^2\times3^2\times5\times7^2)
Explanation: Step 1: Write (8820=180\times49). Step 2: (180=2^2\times3^2\times5) and (49=7^2), so (8820=2^2\times3^2\times5\times7^2). Step 3: Convert 180 and 49 into prime powers.
Correct answer: A. (2^3\times5^2\times7^2)
Explanation: Step 1: Write (9800=8\times1225). Step 2: (8=2^3) and (1225=5^2\times7^2), so (9800=2^3\times5^2\times7^2). Step 3: Do not leave 1225 in the final form.
Correct answer: A. (2^7\times3^4)
Explanation: Step 1: Write (10368=128\times81). Step 2: (128=2^7) and (81=3^4), so (10368=2^7\times3^4). Step 3: Write both 128 and 81 as prime powers.
Correct answer: A. (2^5\times5\times7\times11)
Explanation: Step 1: Write (12320=32\times385). Step 2: (32=2^5) and (385=5\times7\times11), so (12320=2^5\times5\times7\times11). Step 3: Give 385 its complete prime form.
Correct answer: A. (2\times3^3\times5\times7^2)
Explanation: Step 1: Write (13230=270\times49). Step 2: (270=2\times3^3\times5) and (49=7^2), so (13230=2\times3^3\times5\times7^2). Step 3: Do not keep 270 and 49 in the final form.
Correct answer: A. (2^2\times3\times5^2\times7^2)
Explanation: Step 1: Write (14700=300\times49). Step 2: (300=2^2\times3\times5^2) and (49=7^2), so (14700=2^2\times3\times5^2\times7^2). Step 3: Convert 300 into prime powers.
Correct answer: A. (2^5\times3^2\times5\times11)
Explanation: Step 1: Write (15840=32\times495). Step 2: (32=2^5) and (495=3^2\times5\times11), so (15840=2^5\times3^2\times5\times11). Step 3: Give 495 its complete prime form.
Correct answer: A. (2^3\times3^2\times5\times7^2)
Explanation: Step 1: Write (17640=8\times2205). Step 2: (2205=3^2\times5\times7^2), so (17640=2^3\times3^2\times5\times7^2). Step 3: Give 2205 its complete prime form.
Correct answer: A. (2^8\times3^4)
Explanation: Step 1: Write (20736=256\times81). Step 2: (256=2^8) and (81=3^4), so (20736=2^8\times3^4). Step 3: Convert 256 and 81 into prime powers.
Correct answer: A. (2\times3^2\times5^2\times7^2)
Explanation: Step 1: Write (22050=450\times49). Step 2: (450=2\times3^2\times5^2) and (49=7^2), so (22050=2\times3^2\times5^2\times7^2). Step 3: Give 450 its complete prime form.
Correct answer: A. (2^3\times3^2\times5\times7\times11)
Explanation: Step 1: Write (27720=8\times3465). Step 2: (3465=3^2\times5\times7\times11), so (27720=2^3\times3^2\times5\times7\times11). Step 3: Give 3465 its complete prime form.
Correct answer: A. 5
Explanation: Step 1: (15840=32\times495). Step 2: (32=2^5) and (495=3^2\times5\times11), so the power of 2 is 5. Step 3: Comparing gives (a=5).
Correct answer: A. 2
Explanation: Step 1: Write (22050=450\times49). Step 2: (450=2\times3^2\times5^2) and (49=7^2), so the power of 3 is 2. Step 3: Comparing with the given form gives (b=2).
Correct answer: A. 8
Explanation: Step 1: (20736) can be written as (256\times81). Step 2: (256=2^8) and (81=3^4), so (20736=2^8\times3^4). Step 3: Comparing gives (m=8).
Correct answer: A. 5
Explanation: Step 1: For distinct prime factors, exponents are not added. Step 2: The bases are 2, 3, 5, 7, and 11. Step 3: Therefore, there are 5 distinct prime factors.
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