Which is the prime factorisation of 1008?
Correct answer: A
Step 1: Write (1008=16\times63). Step 2: (16=2^4) and (63=3^2\times7), so (1008=2^4\times3^2\times7). Step 3: Give 63 its complete prime form.
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 · prime-factorisation,number-1008,medium
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- (2^4\times3^2\times7)
- (2^3\times3^2\times7)
- (16\times63)
- (2^4\times63)
Medium · Level 7 · prime-factorisation,number-1155,medium
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- (3\times5\times7\times11)
- (11\times105)
- (3\times385)
- (15\times77)
Medium · Level 7 · prime-factorisation,number-1176,medium
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- (2^3\times3\times7^2)
- (2^2\times3^2\times7^2)
- (24\times49)
- (12\times98)
Medium · Level 7 · prime-factorisation,square-number,medium
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- (5^2\times7^2)
- (35\times35)
- (5\times245)
- (7\times175)
Medium · Level 7 · prime-factorisation,number-1296,medium
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- (2^4\times3^4)
- (2^3\times3^5)
- (36\times36)
- (16\times81)
Medium · Level 7 · prime-factorisation,number-1323,medium
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- (3^3\times7^2)
- (3^2\times7^3)
- (27\times49)
- (21\times63)
Medium · Level 7 · prime-factorisation,number-1440,medium
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- (2^5\times3^2\times5)
- (2^4\times3^2\times5)
- (144\times10)
- (32\times45)
Medium · Level 7 · prime-factorisation,number-1470,medium
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- (2\times3\times5\times7^2)
- (2^2\times3\times5\times7)
- (30\times49)
- (14\times105)
Medium · Level 7 · prime-factorisation,cube-number,medium
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- (2^6\times3^3)
- (2^5\times3^4)
- (12^3)
- (64\times27)
Medium · Level 7 · prime-factorisation,number-1800,medium
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- (2^3\times3^2\times5^2)
- (2^2\times3^2\times5^2)
- (18\times100)
- (2\times900)
Medium · Level 7 · prime-factorisation,number-1980,medium
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- (2^2\times3^2\times5\times11)
- (2\times3^2\times5\times11)
- (198\times10)
- (18\times110)
Medium · Level 7 · exponent-comparison,prime-factorisation,medium
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- 3
- 2
- 4
- 5
Medium · Level 7 · exponent-comparison,prime-factorisation,medium
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- 3
- 2
- 4
- 5
Medium · Level 7 · exponent-comparison,square-number,medium
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- 2
- 1
- 3
- 4
Medium · Level 7 · exponent-comparison,number-1800,medium
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- 3
- 2
- 4
- 5
Medium · Level 7 · evaluate-factorisation,number-504,medium
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- 504
- 252
- 1008
- 756
Medium · Level 7 · evaluate-factorisation,number-528,medium
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- 528
- 264
- 1056
- 396
Medium · Level 7 · evaluate-factorisation,number-980,medium
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- 980
- 490
- 1960
- 700
Medium · Level 7 · evaluate-factorisation,number-1728,medium
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- 1728
- 864
- 3456
- 1296
Medium · Level 7 · evaluate-factorisation,number-1980,medium
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- 1980
- 990
- 3960
- 1080
What is the correct prime factorisation of 1155?
Correct answer: A
Step 1: Write (1155=11\times105). Step 2: (105=3\times5\times7), so (1155=3\times5\times7\times11). Step 3: Since 105 is composite, break it further.
View question detailsWhich is the prime factorisation of 1176?
Correct answer: A
Step 1: Write (1176=24\times49). Step 2: (24=2^3\times3) and (49=7^2), so (1176=2^3\times3\times7^2). Step 3: Convert 24 and 49 into prime powers.
View question detailsWhat is the correct prime factorisation of 1225?
Correct answer: A
Step 1: Recognise (1225=35^2). Step 2: Since (35=5\times7), (1225=5^2\times7^2). Step 3: In a square number, prime exponents may be even.
View question detailsWhich is the prime factorisation of 1296?
Correct answer: A
Step 1: Write (1296=16\times81). Step 2: (16=2^4) and (81=3^4), so (1296=2^4\times3^4). Step 3: Do not leave 16 and 81 in the final answer.
View question detailsWhat is the correct prime factorisation of 1323?
Correct answer: A
Step 1: Write (1323=27\times49). Step 2: (27=3^3) and (49=7^2), so (1323=3^3\times7^2). Step 3: Both 27 and 49 are composite, so write them as prime powers.
View question detailsWhich is the prime factorisation of 1440?
Correct answer: A
Step 1: Write (1440=144\times10). Step 2: (144=2^4\times3^2) and (10=2\times5), so (1440=2^5\times3^2\times5). Step 3: The total power of 2 is 5.
View question detailsWhat is the correct 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: Write 49 as (7^2).
View question detailsWhich is the prime factorisation of 1728?
Correct answer: A
Step 1: Recognise (1728=12^3). Step 2: Since (12=2^2\times3), (12^3=2^6\times3^3). Step 3: Since 12 is composite, write powers of 2 and 3 in the final form.
View question detailsWhat is the correct prime factorisation of 1800?
Correct answer: A
Step 1: Write (1800=18\times100). Step 2: (18=2\times3^2) and (100=2^2\times5^2), so (1800=2^3\times3^2\times5^2). Step 3: Give complete prime form to both 18 and 100.
View question detailsWhich is the 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 (840=2^a\times3\times5\times7), what is the value of (a)?
Correct answer: A
Step 1: (840=84\times10). Step 2: (84=2^2\times3\times7) and (10=2\times5), so (840=2^3\times3\times5\times7). Step 3: Comparing gives (a=3).
View question detailsIf (945=3^b\times5\times7), what is the value of (b)?
Correct answer: A
Step 1: (945=27\times35). Step 2: (27=3^3) and (35=5\times7), so (945=3^3\times5\times7). Step 3: Comparing gives (b=3).
View question detailsIf (1225=5^m\times7^2), what is the value of (m)?
Correct answer: A
Step 1: (1225=35^2). Step 2: Since (35=5\times7), (1225=5^2\times7^2). Step 3: Comparing with the given form gives (m=2).
View question detailsIf (1800=2^p\times3^2\times5^2), what is the value of (p)?
Correct answer: A
Step 1: Write (1800=18\times100). Step 2: (18=2\times3^2) and (100=2^2\times5^2), so the total power of 2 is 3. Step 3: Therefore, (p=3).
View question detailsWhich number has prime factorisation (2^3\times3^2\times7)?
Correct answer: A
Step 1: Calculate (2^3=8) and (3^2=9). Step 2: (8\times9\times7=504). Step 3: Evaluate prime powers first, then multiply.
View question detailsWhich number has prime factorisation (2^4\times3\times11)?
Correct answer: A
Step 1: Calculate (2^4=16). Step 2: (16\times3\times11=528). Step 3: While multiplying, complete smaller products first.
View question detailsWhich number has prime factorisation (2^2\times5\times7^2)?
Correct answer: A
Step 1: Calculate (2^2=4) and (7^2=49). Step 2: (4\times5\times49=980). Step 3: Finding powers first reduces mistakes.
View question detailsWhich number has prime factorisation (2^6\times3^3)?
Correct answer: A
Step 1: Calculate (2^6=64) and (3^3=27). Step 2: (64\times27=1728). Step 3: Simplify higher powers separately first.
View question detailsWhich number has prime factorisation (2^2\times3^2\times5\times11)?
Correct answer: A
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.
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