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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. 504
Explanation: Step 1: Calculate (2^3=8) and (3^2=9). Step 2: (8\times9\times7=504). Step 3: Evaluate prime powers first, then multiply.
Correct answer: A. 528
Explanation: Step 1: Calculate (2^4=16). Step 2: (16\times3\times11=528). Step 3: While multiplying, complete smaller products first.
Correct answer: A. 980
Explanation: Step 1: Calculate (2^2=4) and (7^2=49). Step 2: (4\times5\times49=980). Step 3: Finding powers first reduces mistakes.
Correct answer: A. 1728
Explanation: Step 1: Calculate (2^6=64) and (3^3=27). Step 2: (64\times27=1728). Step 3: Simplify higher powers separately first.
Correct answer: A. 1980
Explanation: Step 1: Calculate (2^2=4) and (3^2=9). Step 2: (4\times9\times5\times11=1980). Step 3: Simplifying powers first gives the answer quickly.
Correct answer: A. 672
Explanation: Step 1: (2^5=32). Step 2: (32\times3\times7=672). Step 3: Multiply all factors to convert prime factorisation into the number.
Correct answer: A. 945
Explanation: Step 1: (3^3=27). Step 2: (27\times5\times7=945). Step 3: It is better to simplify the power part first.
Correct answer: A. (2^3\times3^2\times5\times7)
Explanation: Step 1: In prime factorisation, bases must be prime. Step 2: In the first option, bases 2, 3, 5, and 7 are prime. Step 3: 8, 9, 35, and 4 are composite, so the other forms are not final.
Correct answer: A. (2^3\times21\times5)
Explanation: Step 1: Final prime factorisation must not contain a composite factor. Step 2: 21 is composite, so (2^3\times21\times5) is not final form. Step 3: Change 21 into (3\times7).
Correct answer: A. (2^{11})
Explanation: Step 1: Divide 2048 repeatedly by 2. Step 2: Eleven factors of 2 give (2048=2^{11}). Step 3: 4, 32, and 64 are composite, so write (2^{11}) in final form.
Correct answer: A. (3^6)
Explanation: Step 1: Divide 729 repeatedly by 3. Step 2: Six factors of 3 give (729=3^6). Step 3: 9 and 27 are composite, so write a power of 3 in final form.
Correct answer: A. (11^3)
Explanation: Step 1: Write (1331=11\times121). Step 2: (121=11^2), so (1331=11^3). Step 3: Since 121 is composite, write (11^3) in the final form.
Correct answer: A. (7^4)
Explanation: Step 1: (2401) can be written as (49\times49). Step 2: Since (49=7^2), (2401=7^4). Step 3: Since 49 is composite, write the power of 7 in final prime form.
Correct answer: A. (2^2\times5^4)
Explanation: Step 1: Write (2500=25\times100). Step 2: (25=5^2) and (100=2^2\times5^2), so (2500=2^2\times5^4). Step 3: Count the total power of 5 as 4.
Correct answer: A. (2^3\times7^3)
Explanation: Step 1: Recognise (2744=14^3). Step 2: Since (14=2\times7), (2744=2^3\times7^3). Step 3: Since 14 is composite, write prime bases in final form.
Correct answer: A. 720
Explanation: Step 1: Calculate (2^4=16) and (3^2=9). Step 2: (16\times9\times5=720). Step 3: Solving powers first helps find the option quickly.
Correct answer: A. 1800
Explanation: Step 1: Calculate (2^3=8), (3^2=9), and (5^2=25). Step 2: (8\times9\times25=1800). Step 3: Find each power separately and then multiply.
Correct answer: A. 1296
Explanation: Step 1: (2^4=16) and (3^4=81). Step 2: (16\times81=1296). Step 3: In such calculations, simplifying powers first is safer.
Correct answer: A. 2500
Explanation: Step 1: Calculate (2^2=4) and (5^4=625). Step 2: (4\times625=2500). Step 3: Finding the higher power first makes the answer easier.
Correct answer: A. (2^2\times3^3\times5^2)
Explanation: Step 1: Write (2700=27\times100). Step 2: (27=3^3) and (100=2^2\times5^2), so (2700=2^2\times3^3\times5^2). Step 3: Convert both 27 and 100 into prime powers.
Correct answer: A. (2^3\times5\times7\times11)
Explanation: Step 1: Write (3080=8\times385). Step 2: (8=2^3) and (385=5\times7\times11), so (3080=2^3\times5\times7\times11). Step 3: Break 385 into prime form too.
Correct answer: A. (2^3\times3^2\times5\times11)
Explanation: Step 1: Write (3960=36\times110). Step 2: (36=2^2\times3^2) and (110=2\times5\times11), so (3960=2^3\times3^2\times5\times11). Step 3: Count the total power of 2 carefully.
Correct answer: A. 3080
Explanation: Step 1: Calculate (2^3=8). Step 2: (8\times5\times7\times11=3080). Step 3: Whatever the order, the product remains the same.
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 they are not final prime forms.
Correct answer: A. Because 12 is composite
Explanation: Step 1: In final prime factorisation, the base must be prime. Step 2: 12 is composite and (12=2^2\times3). Step 3: Therefore, (12^2) must be changed further into (2^4\times3^2).
