What is the prime factorisation of 1536?
Correct answer: A
Step 1: Write (1536=512\times3). Step 2: (512=2^9), so (1536=2^9\times3). Step 3: Do not keep 512 in the final form; write (2^9).
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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Easy · Level 9 · prime-factorisation,number-1536,easy
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- (2^9\times3)
- (2^8\times3)
- (512\times3)
- (2^6\times24)
Easy · Level 9 · prime-factorisation,number-1080,easy
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- (2^3\times3^3\times5)
- (2^2\times3^3\times5)
- (108\times10)
- (27\times40)
Easy · Level 9 · prime-factorisation,number-1470,easy
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- (2\times3\times5\times7^2)
- (2^2\times3\times5\times7)
- (30\times49)
- (14\times105)
Easy · Level 9 · prime-factorisation,number-1980,easy
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- (2^2\times3^2\times5\times11)
- (2\times3^2\times5\times11)
- (198\times10)
- (18\times110)
Easy · Level 9 · evaluate-factorisation,number-1176,easy
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- 1176
- 588
- 1470
- 2352
Easy · Level 9 · evaluate-factorisation,number-1225,easy
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- 1225
- 875
- 2450
- 6125
Easy · Level 9 · evaluate-factorisation,number-2310,easy
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- 2310
- 1155
- 4620
- 3300
Easy · Level 9 · evaluate-factorisation,number-1800,easy
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- 1800
- 900
- 3600
- 1200
Easy · Level 9 · evaluate-factorisation,number-1296,easy
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- 1296
- 648
- 2592
- 1728
Easy · Level 9 · prime-factorisation,powers,concept-check,easy
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- Writing repeated prime factors shortly and clearly
- Changing the number into addition
- Hiding composite factors
- Writing the answer by guess
Medium · Level 7 · prime-factorisation,concept,medium
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- All factors must be prime
- All factors must be even
- All factors must be two-digit numbers
- Sum of factors must equal the number
Medium · Level 7 · prime-factorisation,number-504,medium
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- (2^3\times3^2\times7)
- (2^2\times3^3\times7)
- (8\times63)
- (2^3\times9\times7)
Medium · Level 7 · prime-factorisation,number-528,medium
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- (2^4\times3\times11)
- (2^3\times3\times22)
- (16\times33)
- (2^4\times33)
Medium · Level 7 · prime-factorisation,number-560,medium
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- (2^4\times5\times7)
- (2^3\times5\times14)
- (16\times35)
- (2^4\times35)
Medium · Level 7 · prime-factorisation,number-630,medium
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- (2\times3^2\times5\times7)
- (2^2\times3\times5\times7)
- (63\times10)
- (2\times9\times35)
Medium · Level 7 · prime-factorisation,number-672,medium
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- (2^5\times3\times7)
- (2^4\times3\times7)
- (32\times21)
- (2^5\times21)
Medium · Level 7 · prime-factorisation,number-700,medium
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- (2^2\times5^2\times7)
- (2\times5^2\times14)
- (7\times100)
- (4\times175)
Medium · Level 7 · prime-factorisation,number-756,medium
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- (2^2\times3^3\times7)
- (2^3\times3^2\times7)
- (27\times28)
- (4\times189)
Medium · Level 7 · prime-factorisation,number-945,medium
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- (3^3\times5\times7)
- (3^2\times5\times7)
- (27\times35)
- (9\times105)
Medium · Level 7 · prime-factorisation,number-980,medium
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- (2^2\times5\times7^2)
- (2\times5\times7^2)
- (98\times10)
- (4\times245)
What is the correct prime factorisation of 1080?
Correct answer: A
Step 1: Write (1080=108\times10). Step 2: (108=2^2\times3^3) and (10=2\times5), so (1080=2^3\times3^3\times5). Step 3: Count powers of 2 and 3 separately.
View question detailsWhich is the prime factorisation of 1470?
Correct answer: A
Step 1: Write (1470=30\times49). Step 2: (30=2\times3\times5) and (49=7^2), so (1470=2\times3\times5\times7^2). Step 3: Convert 49 into (7^2).
View question detailsWhat is the correct prime factorisation of 1980?
Correct answer: A
Step 1: Write (1980=198\times10). Step 2: (198=2\times3^2\times11) and (10=2\times5), so (1980=2^2\times3^2\times5\times11). Step 3: Since 2 appears twice, write (2^2).
View question detailsIf the prime factorisation of a number is (2^3\times3\times7^2), which number is it?
Correct answer: A
Step 1: Calculate (2^3=8) and (7^2=49). Step 2: (8\times3\times49=1176). Step 3: Evaluating powers first makes calculation easier.
View question detailsIf the prime factorisation of a number is (5^2\times7^2), which number is it?
Correct answer: A
Step 1: (5^2=25) and (7^2=49). Step 2: (25\times49=1225). Step 3: Both powers are 2 in this square form, so multiply carefully.
View question detailsWhich number has prime factorisation (2\times3\times5\times7\times11)?
Correct answer: A
Step 1: Multiply all given prime factors. Step 2: (2\times3\times5\times7\times11=2310). Step 3: When no power is written, each prime is taken once.
View question detailsWhich number has prime factorisation (2^3\times3^2\times5^2)?
Correct answer: A
Step 1: Calculate (2^3=8), (3^2=9), and (5^2=25). Step 2: (8\times9\times25=1800). Step 3: Simplify powers first, 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: Calculate (2^4=16) and (3^4=81). Step 2: (16\times81=1296). Step 3: Evaluate prime powers and then multiply.
View question detailsWhat is the main benefit of writing powers in prime factorisation?
Correct answer: A
Step 1: When a prime repeats, powers are used. Step 2: For example, (2\times2\times2) is written as (2^3). Step 3: This makes the answer short, clear, and easy to read in exams.
View question detailsWhat is the most important condition for the final form of prime factorisation?
Correct answer: A
Step 1: In prime factorisation, a number is written as a product of prime numbers. Step 2: If any composite factor remains, the form is not final. Step 3: In exams, write only prime bases and their powers in the final answer.
View question detailsWhat is the correct prime factorisation of 504?
Correct answer: A
Step 1: Write (504=8\times63). Step 2: (8=2^3) and (63=3^2\times7), so (504=2^3\times3^2\times7). Step 3: Do not leave composite forms like 8 and 63 in the final answer.
View question detailsWhich is the prime factorisation of 528?
Correct answer: A
Step 1: (528) can be written as (16\times33). Step 2: (16=2^4) and (33=3\times11), so (528=2^4\times3\times11). Step 3: Since 33 is composite, split it into 3 and 11.
View question detailsWhat is the correct prime factorisation of 560?
Correct answer: A
Step 1: Write (560=16\times35). Step 2: (16=2^4) and (35=5\times7), so (560=2^4\times5\times7). Step 3: Since 35 is composite, write 5 and 7 in the final form.
View question detailsWhich is the prime factorisation of 630?
Correct answer: A
Step 1: Write (630=63\times10). Step 2: (63=3^2\times7) and (10=2\times5), so (630=2\times3^2\times5\times7). Step 3: Do not keep 9 or 35 in the final form.
View question detailsWhat is the correct prime factorisation of 672?
Correct answer: A
Step 1: (672) can be written as (32\times21). Step 2: (32=2^5) and (21=3\times7), so (672=2^5\times3\times7). Step 3: Since 21 is composite, break it further.
View question detailsWhich is the prime factorisation of 700?
Correct answer: A
Step 1: Write (700=7\times100). Step 2: (100=2^2\times5^2), so (700=2^2\times5^2\times7). Step 3: It is necessary to change 100 into prime powers.
View question detailsWhat is the correct prime factorisation of 756?
Correct answer: A
Step 1: Write (756=27\times28). Step 2: (27=3^3) and (28=2^2\times7), so (756=2^2\times3^3\times7). Step 3: Give complete prime form to both parts.
View question detailsWhich is the prime factorisation of 945?
Correct answer: A
Step 1: Write (945=27\times35). Step 2: (27=3^3) and (35=5\times7), so (945=3^3\times5\times7). Step 3: Do not forget to change 27 into (3^3).
View question detailsWhat is the correct prime factorisation of 980?
Correct answer: A
Step 1: Write (980=98\times10). Step 2: (98=2\times7^2) and (10=2\times5), so (980=2^2\times5\times7^2). Step 3: Count the total power of 2 correctly.
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