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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. Writing a number as a product of prime numbers
Explanation: Step 1: In prime factorisation, a number is written as a product of prime numbers. Step 2: For example, 12 can be written as (2^2\times3). Step 3: Keep only prime numbers in the final form.
Correct answer: A. (2^2\times3)
Explanation: Step 1: Divide 12 by 2 to get 6. Step 2: (6=2\times3), so (12=2^2\times3). Step 3: 4 and 6 are composite, so do not keep them in the final answer.
Correct answer: A. (2\times3^2)
Explanation: Step 1: Write 18 as (2\times9). Step 2: Since (9=3^2), (18=2\times3^2). Step 3: Do not leave 9 in the final prime form.
Correct answer: A. (2^2\times5)
Explanation: Step 1: Write (20=4\times5). Step 2: Since (4=2^2), (20=2^2\times5). Step 3: 4 is composite, so write (2^2) in the final form.
Correct answer: A. (2^3\times3)
Explanation: Step 1: Divide 24 repeatedly by 2. Step 2: (24=2\times2\times2\times3=2^3\times3). Step 3: 8 and 6 are composite, so they are not the correct prime form.
Correct answer: A. (2^2\times7)
Explanation: Step 1: Write (28=4\times7). Step 2: Since (4=2^2), (28=2^2\times7). Step 3: In the final answer, write (2^2) instead of 4.
Correct answer: A. (2\times3\times5)
Explanation: Step 1: 30 can be written as (3\times10). Step 2: (10=2\times5), so (30=2\times3\times5). Step 3: Do not keep 6, 10, or 15 in the final prime form.
Correct answer: A. (2^2\times3^2)
Explanation: Step 1: Write (36=4\times9). Step 2: (4=2^2) and (9=3^2), so (36=2^2\times3^2). Step 3: In complete prime form, keep only prime bases.
Correct answer: A. (2\times3\times7)
Explanation: Step 1: Write (42=6\times7). Step 2: (6=2\times3), so (42=2\times3\times7). Step 3: 6 is composite, so do not keep it in the final answer.
Correct answer: A. (3^2\times5)
Explanation: Step 1: Write (45=9\times5). Step 2: Since (9=3^2), (45=3^2\times5). Step 3: 9 is composite, so write (3^2) in the final form.
Correct answer: A. (2^4\times3)
Explanation: Step 1: Divide 48 repeatedly by 2. Step 2: We get (48=2^4\times3). Step 3: 16 and 6 are composite, so they are not final prime answers.
Correct answer: A. (2\times5^2)
Explanation: Step 1: Write (50=2\times25). Step 2: Since (25=5^2), (50=2\times5^2). Step 3: 25 is composite, so write (5^2) in the final form.
Correct answer: A. (2^3\times7)
Explanation: Step 1: Write (56=8\times7). Step 2: Since (8=2^3), (56=2^3\times7). Step 3: 8 is composite, so write (2^3) in the final answer.
Correct answer: A. (2^2\times3\times5)
Explanation: Step 1: Write (60=6\times10). Step 2: (6=2\times3) and (10=2\times5), so (60=2^2\times3\times5). Step 3: 6 and 10 are not final prime forms.
Correct answer: A. (3^2\times7)
Explanation: Step 1: Write (63=9\times7). Step 2: Since (9=3^2), (63=3^2\times7). Step 3: 9 or 21 are composite, so they will not remain in the final answer.
Correct answer: A. (2^3\times3^2)
Explanation: Step 1: Write (72=8\times9). Step 2: (8=2^3) and (9=3^2), so (72=2^3\times3^2). Step 3: In prime factorisation, break 8 and 9 into prime powers.
Correct answer: A. (3\times5^2)
Explanation: Step 1: Write (75=3\times25). Step 2: Since (25=5^2), (75=3\times5^2). Step 3: 25 is composite, so write (5^2) in the final form.
Correct answer: A. (2^2\times3\times7)
Explanation: Step 1: Write (84=4\times21). Step 2: (4=2^2) and (21=3\times7), so (84=2^2\times3\times7). Step 3: Do not keep 4 and 21 in the final answer.
Correct answer: A. (2\times3^2\times5)
Explanation: Step 1: Write (90=9\times10). Step 2: (9=3^2) and (10=2\times5), so (90=2\times3^2\times5). Step 3: Write powers carefully because 3 appears twice.
Correct answer: A. (2^5\times3)
Explanation: Step 1: Divide 96 repeatedly by 2. Step 2: We get (96=2^5\times3). Step 3: 32 means (2^5), but in final prime form write base 2.
Correct answer: A. (2^2\times5^2)
Explanation: Step 1: Write (100=4\times25). Step 2: (4=2^2) and (25=5^2), so (100=2^2\times5^2). Step 3: Convert 4 and 25 into prime powers.
Correct answer: A. (2^2\times3^3)
Explanation: Step 1: Write (108=4\times27). Step 2: (4=2^2) and (27=3^3), so (108=2^2\times3^3). Step 3: Do not forget to change 27 into (3^3).
Correct answer: A. (2^3\times3\times5)
Explanation: Step 1: Write (120=12\times10). Step 2: (12=2^2\times3) and (10=2\times5), so (120=2^3\times3\times5). Step 3: Count the total number of 2s carefully.
Correct answer: A. (5^3)
Explanation: Step 1: Divide 125 by 5 to get 25. Step 2: (25=5^2), so (125=5^3). Step 3: 25 is composite, so the final form is (5^3).
Correct answer: A. (2^4\times3^2)
Explanation: Step 1: Write (144=16\times9). Step 2: (16=2^4) and (9=3^2), so (144=2^4\times3^2). Step 3: Perfect square numbers can have even exponents, so check the powers.
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