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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. 792
Explanation: Step 1: Calculate (2^3=8) and (3^2=9). Step 2: (8\times9\times11=792). Step 3: Solve prime powers first, then multiply.
Correct answer: A. 1680
Explanation: Step 1: Calculate (2^4=16). Step 2: (16\times3\times5\times7=1680). Step 3: When there are four factors, multiply smaller products in order.
Correct answer: A. 1890
Explanation: Step 1: Calculate (3^3=27). Step 2: (2\times27\times5\times7=1890). Step 3: Finding the value of the power first makes calculation simple.
Correct answer: A. 2772
Explanation: Step 1: Calculate (2^2=4) and (3^2=9). Step 2: (4\times9\times7\times11=2772). Step 3: First multiply 4 and 9, then include the remaining factors.
Correct answer: A. 3024
Explanation: Step 1: Calculate (2^4=16) and (3^3=27). Step 2: (16\times27\times7=3024). Step 3: Simplify higher powers separately and multiply.
Correct answer: A. 2100
Explanation: Step 1: (2^2=4) and (5^2=25). Step 2: (4\times3\times25\times7=2100). Step 3: Solving the powers first makes multiplication easier.
Correct answer: A. 2520
Explanation: Step 1: Calculate (2^3=8) and (3^2=9). Step 2: (8\times9\times5\times7=2520). Step 3: First solve powers, then multiply by the remaining factors.
Correct answer: A. (2^4\times3^2\times11)
Explanation: Step 1: In the final form, bases should be prime only. Step 2: In the first option, bases 2, 3, and 11 are prime. Step 3: 16, 9, 99, and 18 are composite, so they are not final forms.
Correct answer: A. (2^2\times25\times7)
Explanation: Step 1: A final prime factorisation should not contain a composite factor like 25. Step 2: Since (25=5^2), (2^2\times25\times7) is not final form. Step 3: Change 25 into (5^2).
Correct answer: A. (2^{12})
Explanation: Step 1: Divide 4096 repeatedly by 2. Step 2: Twelve factors of 2 give (4096=2^{12}). Step 3: 64 and 16 are composite, so write (2^{12}) as the final prime form.
Correct answer: A. (3^8)
Explanation: Step 1: Divide 6561 repeatedly by 3. Step 2: Eight factors of 3 give (6561=3^8). Step 3: 81 and 27 are composite, so write a power of 3 in the final form.
Correct answer: A. (13^3)
Explanation: Step 1: Write (2197=13\times169). Step 2: (169=13^2), so (2197=13^3). Step 3: Since 169 is composite, write (13^3) in the final form.
Correct answer: A. (2\times5^5)
Explanation: Step 1: Write (6250=625\times10). Step 2: (625=5^4) and (10=2\times5), so (6250=2\times5^5). Step 3: Count the total power of 5 as 5.
Correct answer: A. (3^6\times7)
Explanation: Step 1: Write (5103=729\times7). Step 2: (729=3^6), so (5103=3^6\times7). Step 3: Do not leave 729 in the final form; write it as a power of 3.
Correct answer: A. (2^4\times7^3)
Explanation: Step 1: Write (5488=16\times343). Step 2: (16=2^4) and (343=7^3), so (5488=2^4\times7^3). Step 3: Convert 16 and 343 into prime powers.
Correct answer: A. 1584
Explanation: Step 1: Calculate (2^4=16) and (3^2=9). Step 2: (16\times9\times11=1584). Step 3: Solve powers first and then multiply.
Correct answer: A. 1188
Explanation: Step 1: Calculate (2^2=4) and (3^3=27). Step 2: (4\times27\times11=1188). Step 3: Finding the value of powers first is the right method.
Correct answer: A. 1350
Explanation: Step 1: Calculate (3^3=27) and (5^2=25). Step 2: (2\times27\times25=1350). Step 3: Simplifying the two powers first makes multiplication easy.
Correct answer: A. 2772
Explanation: Step 1: Calculate (2^2=4) and (3^2=9). Step 2: (4\times9\times7\times11=2772). Step 3: Move step by step while multiplying.
Correct answer: A. (2^3\times3\times5^2\times7)
Explanation: Step 1: Write (4200=42\times100). Step 2: (42=2\times3\times7) and (100=2^2\times5^2), so (4200=2^3\times3\times5^2\times7). Step 3: Count the powers of 2 and 5 carefully.
Correct answer: A. (2^2\times3\times5\times7\times11)
Explanation: Step 1: Write (4620=42\times110). Step 2: (42=2\times3\times7) and (110=2\times5\times11), so (4620=2^2\times3\times5\times7\times11). Step 3: Since 2 appears twice, write (2^2).
Correct answer: A. (2^3\times3^3\times5^2)
Explanation: Step 1: Write (5400=54\times100). Step 2: (54=2\times3^3) and (100=2^2\times5^2), so (5400=2^3\times3^3\times5^2). Step 3: Break both 54 and 100 completely.
Correct answer: A. 4620
Explanation: Step 1: Calculate (2^2=4). Step 2: (4\times3\times5\times7\times11=4620). Step 3: When there are many factors, multiply in pairs.
Correct answer: A. (2^{13})
Explanation: Step 1: Divide 8192 repeatedly by 2. Step 2: Thirteen factors of 2 give (8192=2^{13}). Step 3: 64 and 16 are composite, so write the power of 2 in final prime form.
Correct answer: A. Because 18 and 100 are composite numbers
Explanation: Step 1: In prime factorisation, every final factor must be prime. Step 2: (18=2\times3^2) and (100=2^2\times5^2), so both are composite. Step 3: (18\times100) must be changed further into (2^3\times3^2\times5^2).
