Which number has prime factorisation (2^3\times3^2\times11)?
Correct answer: A
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.
Mathematics
Prime Factorisation
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.
TOPIC PRACTICE
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Medium · Level 6
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- 792
- 396
- 1188
- 1584
Medium · Level 6
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- 825
- 550
- 1650
- 275
Medium · Level 6
View options
- 864
- 432
- 1728
- 1296
Medium · Level 6
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- 924
- 462
- 1848
- 1386
Medium · Level 6
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- 3120
- 1560
- 6240
- 2340
Medium · Level 6
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- 2640
- 1320
- 5280
- 1980
Medium · Level 6
View options
- 2835
- 945
- 5670
- 2025
Medium · Level 6
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- (2^2\times3^4\times7)
- (4\times81\times7)
- (2^2\times567)
- (12\times189)
Medium · Level 6
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- (2^4\times195)
- (2^4\times3\times5\times13)
- (3^4\times5\times7)
- (2\times5^2\times7^2)
Medium · Level 6
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- (2^5\times3^5)
- (2^4\times3^5)
- (32\times243)
- (6^5)
Medium · Level 6
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- (2^4\times5^4)
- (2^5\times5^3)
- (10^4)
- (100\times100)
Medium · Level 6
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- (17^3)
- (17^2)
- (289\times17)
- (4913\times1)
Medium · Level 6
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- (2^2\times5^5)
- (2\times5^5)
- (125\times100)
- (4\times3125)
Medium · Level 6
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- (2\times3^6\times7)
- (2\times3^5\times7)
- (2\times5103)
- (1458\times7)
Medium · Level 6
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- (2^3\times5\times7^3)
- (2^4\times5\times7^2)
- (40\times343)
- (8\times1715)
Medium · Level 6
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- 2016
- 1008
- 4032
- 1344
Medium · Level 6
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- 2205
- 735
- 4410
- 1470
Medium · Level 6
View options
- 2268
- 1134
- 4536
- 3402
Medium · Level 6
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- 2640
- 1320
- 5280
- 3960
Medium · Level 6
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- (2^4\times3^3\times11)
- (2^3\times3^3\times11)
- (16\times297)
- (2^4\times27\times11)
Medium · Level 6
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- (2\times3^2\times5^2\times13)
- (2^2\times3\times5^2\times13)
- (58.5\times100)
- (18\times325)
Medium · Level 6
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- (2^3\times3^3\times5\times7)
- (2^2\times3^3\times5\times7)
- (756\times10)
- (8\times945)
Medium · Level 6
View options
- 5850
- 2925
- 11700
- 3900
Medium · Level 6
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- (2^{14})
- (2^{13})
- (128^2)
- (16^4)
Medium · Level 6
View options
- Because 25 is composite
- Because 7 is not prime
- Because writing powers is wrong
- Because multiplication cannot be used
Which number has prime factorisation (3\times5^2\times11)?
Correct answer: A
Step 1: Calculate (5^2=25). Step 2: (3\times25\times11=825). Step 3: It is useful to simplify the power part first.
Which number has prime factorisation (2^5\times3^3)?
Correct answer: A
Step 1: Calculate (2^5=32) and (3^3=27). Step 2: (32\times27=864). Step 3: Simplify both powers separately.
Which number has prime factorisation (2^2\times3\times7\times11)?
Correct answer: A
Step 1: Calculate (2^2=4). Step 2: (4\times3\times7\times11=924). Step 3: With many factors, multiply in pairs.
Which number has prime factorisation (2^4\times3\times5\times13)?
Correct answer: A
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.
If (n=2^4\times3\times5\times11), what is the value of (n)?
Correct answer: A
Step 1: (2^4=16). Step 2: (16\times3\times5\times11=2640). Step 3: Multiply all factors to get the number from prime form.
If (m=3^4\times5\times7), what is the value of (m)?
Correct answer: A
Step 1: (3^4=81). Step 2: (81\times5\times7=2835). Step 3: Simplifying the power first keeps the calculation clear.
Which option gives the final form using only prime factors?
Correct answer: A
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.
Which option is not a final prime factorisation?
Correct answer: A
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.
What is the prime factorisation of 7776?
Correct answer: A
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.
What is the correct prime factorisation of 10000?
Correct answer: A
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.
Which is the prime factorisation of 4913?
Correct answer: A
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.
What is the correct prime factorisation of 12500?
Correct answer: A
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.
Which is the prime factorisation of 10206?
Correct answer: A
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.
What is the correct prime factorisation of 13720?
Correct answer: A
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.
If a number is formed from (2^5\times3^2\times7), which number will it be?
Correct answer: A
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.
If the prime factorisation of a number is (3^2\times5\times7^2), which number is it?
Correct answer: A
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.
If the prime factorisation of a number is (2^2\times3^4\times7), which number is it?
Correct answer: A
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.
If (2^4\times3\times5\times11) is the prime factorisation of a number, what is the number?
Correct answer: A
Step 1: Calculate (2^4=16). Step 2: (16\times3\times5\times11=2640). Step 3: Do multiplication in small steps to avoid mistakes.
What is the correct prime factorisation of 4752?
Correct answer: A
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.
Which is the prime factorisation of 5850?
Correct answer: A
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.
What is the correct prime factorisation of 7560?
Correct answer: A
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.
Which number has prime factorisation (2\times3^2\times5^2\times13)?
Correct answer: A
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.
What is the prime factorisation of 16384?
Correct answer: A
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.
Why is (25^2\times7) not considered a final form in prime factorisation?
Correct answer: A
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).
QUIZ COMPLETE