If (n=2^5\times3\times7), what is the value of (n)?
Correct answer: A
Step 1: (2^5=32). Step 2: (32\times3\times7=672). Step 3: Multiply all factors to convert prime factorisation into the number.
View question detailsMathematics
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.
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Medium · Level 7 · evaluate-factorisation,powers,medium
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- 672
- 336
- 1008
- 504
Medium · Level 7 · evaluate-factorisation,powers,medium
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- 945
- 315
- 1890
- 735
Medium · Level 7 · prime-factors,concept-check,medium
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- (2^3\times3^2\times5\times7)
- (8\times9\times5\times7)
- (2^3\times9\times35)
- (4\times3^2\times5\times7)
Medium · Level 7 · prime-factorisation,not-final-form,medium
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- (2^3\times21\times5)
- (2^3\times3\times5\times7)
- (2^2\times3^2\times7)
- (3^3\times5\times7)
Medium · Level 7 · prime-factorisation,power-of-two,medium
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- (2^{11})
- (2^{10})
- (4^5\times2)
- (32\times64)
Medium · Level 7 · prime-factorisation,power-of-three,medium
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- (3^6)
- (3^5)
- (9^3)
- (27^2)
Medium · Level 7 · prime-factorisation,cube-number,medium
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- (11^3)
- (11^2)
- (121\times11)
- (1331\times1)
Medium · Level 7 · prime-factorisation,power-of-seven,medium
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- (7^4)
- (7^3)
- (49^2)
- (7\times343)
Medium · Level 7 · prime-factorisation,number-2500,medium
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- (2^2\times5^4)
- (2^4\times5^2)
- (25\times100)
- (50\times50)
Medium · Level 7 · prime-factorisation,cube-number,medium
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- (2^3\times7^3)
- (14^3)
- (2^2\times7^4)
- (8\times343)
Medium · Level 7 · evaluate-factorisation,mcq-pattern,medium
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- 720
- 360
- 1440
- 1080
Medium · Level 7 · evaluate-factorisation,number-1800,medium
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- 1800
- 900
- 3600
- 1200
Medium · Level 7 · evaluate-factorisation,number-1296,medium
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- 1296
- 648
- 2592
- 1728
Medium · Level 7 · evaluate-factorisation,number-2500,medium
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- 2500
- 1250
- 5000
- 625
Medium · Level 7 · prime-factorisation,number-2700,medium
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- (2^2\times3^3\times5^2)
- (2\times3^3\times5^2)
- (27\times100)
- (2^2\times3^2\times5^3)
Medium · Level 7 · prime-factorisation,number-3080,medium
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- (2^3\times5\times7\times11)
- (2^2\times5\times7\times11)
- (28\times110)
- (8\times385)
Medium · Level 7 · prime-factorisation,number-3960,medium
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- (2^3\times3^2\times5\times11)
- (2^2\times3^2\times5\times11)
- (36\times110)
- (2^3\times9\times55)
Medium · Level 7 · evaluate-factorisation,number-3080,medium
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- 3080
- 1540
- 6160
- 3850
Medium · Level 7 · prime-factorisation,power-of-two,medium
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- (2^{12})
- (2^{11})
- (64^2)
- (16^3)
Medium · Level 7 · prime-factorisation,concept-check,medium
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- Because 12 is composite
- Because 12 is prime
- Because square numbers cannot be factorised
- Because writing powers is wrong
If (m=3^3\times5\times7), what is the value of (m)?
Correct answer: A
Step 1: (3^3=27). Step 2: (27\times5\times7=945). Step 3: It is better to simplify the power part first.
View question detailsWhich option contains only prime factors?
Correct answer: A
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.
View question detailsWhich option is not a final prime factorisation?
Correct answer: A
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).
View question detailsWhat is the prime factorisation of 2048?
Correct answer: A
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.
View question detailsWhat is the correct prime factorisation of 729?
Correct answer: A
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.
View question detailsWhich is the prime factorisation of 1331?
Correct answer: A
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.
View question detailsWhat is the correct prime factorisation of 2401?
Correct answer: A
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.
View question detailsWhich is the prime factorisation of 2500?
Correct answer: A
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.
View question detailsWhat is the correct prime factorisation of 2744?
Correct answer: A
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.
View question detailsIf a number is formed from (2^4\times3^2\times5), which number will it be?
Correct answer: A
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.
View question detailsIf the prime factorisation of a number is (2^3\times3^2\times5^2), which number is it?
Correct answer: A
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.
View question detailsIf the prime factorisation of a number is (2^4\times3^4), which number is it?
Correct answer: A
Step 1: (2^4=16) and (3^4=81). Step 2: (16\times81=1296). Step 3: In such calculations, simplifying powers first is safer.
View question detailsIf (2^2\times5^4) is the prime factorisation of a number, what is the number?
Correct answer: A
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.
View question detailsWhat is the correct prime factorisation of 2700?
Correct answer: A
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.
View question detailsWhich is the prime factorisation of 3080?
Correct answer: A
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.
View question detailsWhat is the correct prime factorisation of 3960?
Correct answer: A
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.
View question detailsWhich number has prime factorisation (2^3\times5\times7\times11)?
Correct answer: A
Step 1: Calculate (2^3=8). Step 2: (8\times5\times7\times11=3080). Step 3: Whatever the order, the product remains the same.
View question detailsWhat is the prime factorisation of 4096?
Correct answer: A
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.
View question detailsWhy is (12^2) not considered a final form in prime factorisation?
Correct answer: A
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).
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