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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. Powers of the same prime base
Explanation: Step 1: In prime factorisation, identify the bases first. Step 2: Powers of the same base are compared, such as power of 2 with power of 2 and power of 3 with power of 3. Step 3: In exams, do not compare powers directly when bases are different.
Correct answer: A. (2\times3^2\times5\times13)
Explanation: Step 1: Write (1170=117\times10). Step 2: (117=3^2\times13) and (10=2\times5), so (1170=2\times3^2\times5\times13). Step 3: Do not keep 117 and 10 in the final form.
Correct answer: A. (3^5\times5)
Explanation: Step 1: Write (1215=243\times5). Step 2: Since (243=3^5), (1215=3^5\times5). Step 3: 243 is composite, so write it as a power of 3 in final prime form.
Correct answer: A. (2^6\times3\times7)
Explanation: Step 1: Write (1344=64\times21). Step 2: (64=2^6) and (21=3\times7), so (1344=2^6\times3\times7). Step 3: Since 21 is composite, split it into 3 and 7.
Correct answer: A. (3^3\times5\times11)
Explanation: Step 1: Write (1485=135\times11). Step 2: (135=3^3\times5), so (1485=3^3\times5\times11). Step 3: Give 135 its complete prime form.
Correct answer: A. (2^2\times3^4\times5)
Explanation: Step 1: Write (1620=162\times10). Step 2: (162=2\times3^4) and (10=2\times5), so (1620=2^2\times3^4\times5). Step 3: Count the total power of 2 correctly.
Correct answer: A. (2^3\times3\times7\times11)
Explanation: Step 1: Write (1848=8\times231). Step 2: (8=2^3) and (231=3\times7\times11), so (1848=2^3\times3\times7\times11). Step 3: Give 231 its complete prime form.
Correct answer: A. (3\times5^4)
Explanation: Step 1: Write (1875=3\times625). Step 2: Since (625=5^4), (1875=3\times5^4). Step 3: Do not leave 625 in the final form; write (5^4).
Correct answer: A. (2^5\times3^2\times7)
Explanation: Step 1: Write (2016=32\times63). Step 2: (32=2^5) and (63=3^2\times7), so (2016=2^5\times3^2\times7). Step 3: Convert 63 into prime powers.
Correct answer: A. (3^2\times5\times7^2)
Explanation: Step 1: Write (2205=45\times49). Step 2: (45=3^2\times5) and (49=7^2), so (2205=3^2\times5\times7^2). Step 3: Give complete prime form to 45 and 49.
Correct answer: A. (2^2\times3^4\times7)
Explanation: Step 1: Write (2268=4\times567). Step 2: (4=2^2) and (567=3^4\times7), so (2268=2^2\times3^4\times7). Step 3: Convert 567 into complete prime form.
Correct answer: A. (2^2\times3^2\times5\times13)
Explanation: Step 1: Write (2340=234\times10). Step 2: (234=2\times3^2\times13) and (10=2\times5), so (2340=2^2\times3^2\times5\times13). Step 3: The power of 2 becomes 2.
Correct answer: A. (2\times5^2\times7^2)
Explanation: Step 1: Write (2450=2\times1225). Step 2: (1225=5^2\times7^2), so (2450=2\times5^2\times7^2). Step 3: Convert 1225 into prime powers.
Correct answer: A. (2^4\times3\times5\times11)
Explanation: Step 1: Write (2640=16\times165). Step 2: (16=2^4) and (165=3\times5\times11), so (2640=2^4\times3\times5\times11). Step 3: Break 165 further.
Correct answer: A. (3^4\times5\times7)
Explanation: Step 1: Write (2835=81\times35). Step 2: (81=3^4) and (35=5\times7), so (2835=3^4\times5\times7). Step 3: Change 81 into (3^4).
Correct answer: A. (2^4\times3\times5\times13)
Explanation: Step 1: Write (3120=16\times195). Step 2: (16=2^4) and (195=3\times5\times13), so (3120=2^4\times3\times5\times13). Step 3: Give 195 its complete prime form.
Correct answer: A. (2\times3^5\times7)
Explanation: Step 1: Write (3402=2\times1701). Step 2: (1701=3^5\times7), so (3402=2\times3^5\times7). Step 3: Convert 1701 into prime form using 3 and 7.
Correct answer: A. (2^3\times3^2\times7^2)
Explanation: Step 1: Write (3528=72\times49). Step 2: (72=2^3\times3^2) and (49=7^2), so (3528=2^3\times3^2\times7^2). Step 3: Convert 72 and 49 into prime powers.
Correct answer: A. (3^6\times5)
Explanation: Step 1: Write (3645=729\times5). Step 2: Since (729=3^6), (3645=3^6\times5). Step 3: 729 should not be left in the final form.
Correct answer: A. (2^4\times3^5)
Explanation: Step 1: Write (3888=16\times243). Step 2: (16=2^4) and (243=3^5), so (3888=2^4\times3^5). Step 3: Change 243 into a power of 3.
Correct answer: A. (3^4\times7^2)
Explanation: Step 1: Write (3969=81\times49). Step 2: (81=3^4) and (49=7^2), so (3969=3^4\times7^2). Step 3: Write both parts as prime powers.
Correct answer: A. 5
Explanation: Step 1: Write (2016=32\times63). Step 2: (32=2^5) and (63=3^2\times7), so (2016=2^5\times3^2\times7). Step 3: Comparing gives (a=5).
Correct answer: A. 2
Explanation: Step 1: (2205=45\times49). Step 2: (45=3^2\times5) and (49=7^2), so (2205=3^2\times5\times7^2). Step 3: Comparing gives (b=2).
Correct answer: A. 2
Explanation: Step 1: (2450=2\times1225). Step 2: (1225=5^2\times7^2), so (2450=2\times5^2\times7^2). Step 3: Comparing with the given form gives (m=2).
Correct answer: A. 4
Explanation: Step 1: Write (3888=16\times243). Step 2: (16=2^4) and (243=3^5), so the power of 2 is 4. Step 3: Comparing gives (p=4).
