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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: First solve the powers, then multiply by 11.
Correct answer: A. 825
Explanation: Step 1: Calculate (5^2=25). Step 2: (3\times25\times11=825). Step 3: It is useful to simplify the power part first.
Correct answer: A. 864
Explanation: Step 1: Calculate (2^5=32) and (3^3=27). Step 2: (32\times27=864). Step 3: Simplify both powers separately.
Correct answer: A. 924
Explanation: Step 1: Calculate (2^2=4). Step 2: (4\times3\times7\times11=924). Step 3: With many factors, multiply in pairs.
Correct answer: A. 3120
Explanation: Step 1: Calculate (2^4=16). Step 2: (16\times3\times5\times13=3120). Step 3: It is easy to first treat (3\times5\times13) as 195 and multiply.
Correct answer: A. 2640
Explanation: Step 1: (2^4=16). Step 2: (16\times3\times5\times11=2640). Step 3: Multiply all factors to get the number from prime form.
Correct answer: A. 2835
Explanation: Step 1: (3^4=81). Step 2: (81\times5\times7=2835). Step 3: Simplifying the power first keeps the calculation clear.
Correct answer: A. (2^2\times3^4\times7)
Explanation: Step 1: In final prime form, bases should be prime. Step 2: In the first option, 2, 3, and 7 are prime bases. Step 3: 4, 81, 567, 12, and 189 are composite, so they are not final forms.
Correct answer: A. (2^4\times195)
Explanation: Step 1: Final prime factorisation must not contain a composite factor. Step 2: 195 is composite and (195=3\times5\times13). Step 3: Therefore, (2^4\times195) is not final form.
Correct answer: A. (2^5\times3^5)
Explanation: Step 1: Write (7776=32\times243). Step 2: (32=2^5) and (243=3^5), so (7776=2^5\times3^5). Step 3: 32 and 243 are composite, so write prime bases in the final form.
Correct answer: A. (2^4\times5^4)
Explanation: Step 1: (10000) can be written as (10^4). Step 2: Since (10=2\times5), (10^4=2^4\times5^4). Step 3: 10 is composite, so write powers of 2 and 5 in the final form.
Correct answer: A. (17^3)
Explanation: Step 1: Write (4913=17\times289). Step 2: (289=17^2), so (4913=17^3). Step 3: Since 289 is composite, write (17^3) in the final form.
Correct answer: A. (2^2\times5^5)
Explanation: Step 1: Write (12500=125\times100). Step 2: (125=5^3) and (100=2^2\times5^2), so (12500=2^2\times5^5). Step 3: Count the total power of 5 as 5.
Correct answer: A. (2\times3^6\times7)
Explanation: Step 1: Write (10206=2\times5103). Step 2: (5103=3^6\times7), so (10206=2\times3^6\times7). Step 3: Convert 5103 into prime powers.
Correct answer: A. (2^3\times5\times7^3)
Explanation: Step 1: Write (13720=40\times343). Step 2: (40=2^3\times5) and (343=7^3), so (13720=2^3\times5\times7^3). Step 3: Write 40 and 343 in prime form.
Correct answer: A. 2016
Explanation: Step 1: Calculate (2^5=32) and (3^2=9). Step 2: (32\times9\times7=2016). Step 3: Solving powers first gives the answer quickly.
Correct answer: A. 2205
Explanation: Step 1: Calculate (3^2=9) and (7^2=49). Step 2: (9\times5\times49=2205). Step 3: Simplify the two powers first and multiply.
Correct answer: A. 2268
Explanation: Step 1: Calculate (2^2=4) and (3^4=81). Step 2: (4\times81\times7=2268). Step 3: Simplifying the higher power first is the right method.
Correct answer: A. 2640
Explanation: Step 1: Calculate (2^4=16). Step 2: (16\times3\times5\times11=2640). Step 3: Do multiplication in small steps to avoid mistakes.
Correct answer: A. (2^4\times3^3\times11)
Explanation: Step 1: Write (4752=16\times297). Step 2: (16=2^4) and (297=3^3\times11), so (4752=2^4\times3^3\times11). Step 3: Give 297 its complete prime form.
Correct answer: A. (2\times3^2\times5^2\times13)
Explanation: Step 1: Write (5850=18\times325). Step 2: (18=2\times3^2) and (325=5^2\times13), so (5850=2\times3^2\times5^2\times13). Step 3: Avoid decimal forms and use whole factors.
Correct answer: A. (2^3\times3^3\times5\times7)
Explanation: Step 1: Write (7560=756\times10). Step 2: (756=2^2\times3^3\times7) and (10=2\times5), so (7560=2^3\times3^3\times5\times7). Step 3: Count the total power of 2 as 3.
Correct answer: A. 5850
Explanation: Step 1: Calculate (3^2=9) and (5^2=25). Step 2: (2\times9\times25\times13=5850). Step 3: First do (9\times25=225), then multiply the rest.
Correct answer: A. (2^{14})
Explanation: Step 1: Divide 16384 repeatedly by 2. Step 2: Fourteen factors of 2 give (16384=2^{14}). Step 3: 128 and 16 are composite, so write the power of 2 in final prime form.
Correct answer: A. Because 25 is composite
Explanation: Step 1: In final prime factorisation, the base must be prime. Step 2: 25 is composite and (25=5^2). Step 3: Therefore, (25^2\times7) must be changed into (5^4\times7).
