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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. 2
Explanation: Step 1: The prime factorisation of 132 is (2^2\times3\times11). Step 2: In the given form, the power of 2 is (a). Step 3: Comparing gives (a=2).
Correct answer: A. 2
Explanation: Step 1: The prime factorisation of 150 is (2\times3\times5^2). Step 2: In the given form, the power of 5 is (b). Step 3: Comparing gives (b=2).
Correct answer: A. 168
Explanation: Step 1: Calculate (2^3=8). Step 2: (8\times3\times7=168). Step 3: To get the number from prime factorisation, multiply all factors.
Correct answer: A. 270
Explanation: Step 1: Calculate (3^3=27). Step 2: (2\times27\times5=270). Step 3: Evaluating the power first makes calculation easy.
Correct answer: A. 240
Explanation: Step 1: (2^4=16). Step 2: (16\times3\times5=240). Step 3: Multiply to get the number from prime form.
Correct answer: A. 315
Explanation: Step 1: Calculate (3^2=9). Step 2: (9\times5\times7=315). Step 3: Simplify the factor with a power first.
Correct answer: A. (2\times3\times7\times11)
Explanation: Step 1: In final prime factorisation, every factor must be prime. Step 2: 2, 3, 7, and 11 are all prime. Step 3: 6, 21, and 33 are composite, so they cannot remain in final form.
Correct answer: A. (6\times5^2)
Explanation: Step 1: Final prime factorisation must not contain a composite factor. Step 2: 6 is composite, so (6\times5^2) is not final form. Step 3: Change 6 into (2\times3).
Correct answer: A. (2^8)
Explanation: Step 1: Divide 256 repeatedly by 2. Step 2: Eight factors of 2 give (256=2^8). Step 3: 4 and 16 are composite, so do not write them in final prime form.
Correct answer: A. (3^5)
Explanation: Step 1: Divide 243 repeatedly by 3. Step 2: Five factors of 3 give (243=3^5). Step 3: 9 and 27 are composite, so keep prime base 3.
Correct answer: A. (13^2)
Explanation: Step 1: 169 is a square number. Step 2: (169=13\times13=13^2). Step 3: Since 13 is prime, (13^2) is the correct prime factorisation.
Correct answer: A. (17^2)
Explanation: Step 1: (289=17\times17). Step 2: Since 17 is prime, (289=17^2). Step 3: In a square number, the same prime appears twice.
Correct answer: A. (2^9)
Explanation: Step 1: Divide 512 repeatedly by 2. Step 2: Nine factors of 2 give (512=2^9). Step 3: 8, 16, and 32 are composite, so write the power of 2 in final prime form.
Correct answer: A. (5^4)
Explanation: Step 1: (625) can be written as (25\times25). Step 2: (25=5^2), so (625=5^4). Step 3: 25 is composite, so write the power of 5 in final form.
Correct answer: A. (2^3\times3^3)
Explanation: Step 1: Write (216=8\times27). Step 2: (8=2^3) and (27=3^3), so (216=2^3\times3^3). Step 3: 6, 8, and 27 are composite, so write prime bases in final form.
Correct answer: A. (2^7)
Explanation: Step 1: Divide 128 repeatedly by 2. Step 2: Seven factors of 2 give (128=2^7). Step 3: 4, 8, and 16 are composite, so write (2^7) in final form.
Correct answer: A. (2^2\times3^3\times5)
Explanation: Step 1: Write (540=54\times10). Step 2: (54=2\times3^3) and (10=2\times5), so (540=2^2\times3^3\times5). Step 3: Break 54 completely into prime form.
Correct answer: A. (2^2\times3\times7^2)
Explanation: Step 1: Write (588=12\times49). Step 2: (12=2^2\times3) and (49=7^2), so (588=2^2\times3\times7^2). Step 3: Convert 12 and 49 into prime powers.
Correct answer: A. (2^2\times3\times5\times11)
Explanation: Step 1: Write (660=66\times10). Step 2: (66=2\times3\times11) and (10=2\times5), so (660=2^2\times3\times5\times11). Step 3: Since 2 appears twice, write (2^2).
Correct answer: A. 132
Explanation: Step 1: Calculate (2^2=4). Step 2: (4\times3\times11=132). Step 3: Multiply all factors to get the number from prime factorisation.
Correct answer: A. 225
Explanation: Step 1: Calculate (3^2=9) and (5^2=25). Step 2: (9\times25=225). Step 3: Simplify powers first and then multiply.
Correct answer: A. 210
Explanation: Step 1: All prime factors are given. Step 2: (2\times3\times5\times7=210). Step 3: When no power is written, each prime is taken once.
Correct answer: A. 252
Explanation: Step 1: Calculate (2^2=4) and (3^2=9). Step 2: (4\times9\times7=252). Step 3: Evaluate prime powers and then multiply.
Correct answer: A. 400
Explanation: Step 1: Calculate (2^4=16) and (5^2=25). Step 2: (16\times25=400). Step 3: Finding powers first makes the calculation easier.
Correct answer: A. Because 1 is not a prime number
Explanation: Step 1: A prime number has exactly two factors. Step 2: 1 has only one factor, so 1 is not prime. Step 3: Do not write 1 as a final factor in prime factorisation.
