What is the correct prime factorisation of 486?
Correct answer: A
Step 1: Write (486=2\times243). Step 2: Since (243=3^5), (486=2\times3^5). Step 3: Do not leave 243 in the final answer; write it as a power of 3.
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-486,easy
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- (2\times3^5)
- (2^2\times3^4)
- (6\times81)
- (18\times27)
Easy · Level 9 · prime-factorisation,number-600,easy
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- (2^3\times3\times5^2)
- (2^2\times3\times5^2)
- (6\times100)
- (2\times300)
Easy · Level 9 · prime-factorisation,number-675,easy
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- (3^3\times5^2)
- (3^2\times5^3)
- (27\times25)
- (9\times75)
Easy · Level 9 · prime-factorisation,number-720,easy
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- (2^4\times3^2\times5)
- (2^3\times3^2\times5)
- (72\times10)
- (8\times90)
Easy · Level 9 · prime-factorisation,number-756,easy
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- (2^2\times3^3\times7)
- (2^3\times3^2\times7)
- (27\times28)
- (4\times189)
Easy · Level 9 · prime-factorisation,square-number,easy
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- (2^4\times7^2)
- (2^3\times7^2)
- (28\times28)
- (16\times49)
Easy · Level 9 · prime-factorisation,number-840,easy
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- (2^3\times3\times5\times7)
- (2^2\times3\times5\times7)
- (84\times10)
- (21\times40)
Easy · Level 9 · prime-factorisation,square-number,easy
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- (2^2\times3^2\times5^2)
- (2^3\times3^2\times5)
- (30\times30)
- (9\times100)
Easy · Level 9 · prime-factorisation,number-945,easy
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- (3^3\times5\times7)
- (3^2\times5\times7)
- (27\times35)
- (9\times105)
Easy · Level 9 · prime-factorisation,cube-number,easy
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- (2^3\times5^3)
- (2^2\times5^3)
- (10^3)
- (100\times10)
Easy · Level 9 · prime-factorisation,power-of-two,easy
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- (2^{10})
- (2^9)
- (4^5)
- (32^2)
Easy · Level 9 · prime-factorisation,number-1155,easy
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- (3\times5\times7\times11)
- (11\times105)
- (3\times385)
- (15\times77)
Easy · Level 9 · prime-factorisation,number-1176,easy
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- (2^3\times3\times7^2)
- (2^2\times3^2\times7^2)
- (24\times49)
- (12\times98)
Easy · Level 9 · prime-factorisation,square-number,easy
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- (5^2\times7^2)
- (35\times35)
- (5\times245)
- (7\times175)
Easy · Level 9 · prime-factorisation,square-number,easy
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- (2^4\times3^4)
- (36\times36)
- (2^3\times3^5)
- (16\times81)
Easy · Level 9 · prime-factorisation,number-1323,easy
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- (3^3\times7^2)
- (3^2\times7^3)
- (27\times49)
- (21\times63)
Easy · Level 9 · prime-factorisation,number-1440,easy
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- (2^5\times3^2\times5)
- (2^4\times3^2\times5)
- (144\times10)
- (32\times45)
Easy · Level 9 · prime-factorisation,number-1575,easy
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- (3^2\times5^2\times7)
- (3\times5^3\times7)
- (15\times105)
- (225\times7)
Easy · Level 9 · prime-factorisation,cube-number,easy
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- (2^6\times3^3)
- (12^3)
- (2^5\times3^4)
- (64\times27)
Easy · Level 9 · prime-factorisation,square-number,easy
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- (2^2\times3^2\times7^2)
- (42\times42)
- (2^3\times3^2\times7)
- (4\times441)
Which is the prime factorisation of 600?
Correct answer: A
Step 1: Write (600=6\times100). Step 2: (6=2\times3) and (100=2^2\times5^2), so (600=2^3\times3\times5^2). Step 3: Be careful while counting the total power of 2.
View question detailsWhat is the correct prime factorisation of 675?
Correct answer: A
Step 1: Write (675=27\times25). Step 2: (27=3^3) and (25=5^2), so (675=3^3\times5^2). Step 3: 27 and 25 are composite, so convert them into prime powers.
View question detailsWhich is the prime factorisation of 720?
Correct answer: A
Step 1: Write (720=72\times10). Step 2: (72=2^3\times3^2) and (10=2\times5), so (720=2^4\times3^2\times5). Step 3: Break 72 completely into prime form.
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: Convert 28 into (2^2\times7).
View question detailsWhich is the prime factorisation of 784?
Correct answer: A
Step 1: Recognise (784=28^2). Step 2: Since (28=2^2\times7), (784=2^4\times7^2). Step 3: In a square number, exponents may be even, so check the powers.
View question detailsWhat is the correct prime factorisation of 840?
Correct answer: A
Step 1: Write (840=84\times10). Step 2: (84=2^2\times3\times7) and (10=2\times5), so (840=2^3\times3\times5\times7). Step 3: Break all composite factors down to primes.
View question detailsWhich is the prime factorisation of 900?
Correct answer: A
Step 1: Write (900=9\times100). Step 2: (9=3^2) and (100=2^2\times5^2), so (900=2^2\times3^2\times5^2). Step 3: 900 is a square number, so even exponents appear.
View question detailsWhat is the correct 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 detailsWhich is the prime factorisation of 1000?
Correct answer: A
Step 1: (1000) can be written as (10^3). Step 2: Since (10=2\times5), (1000=2^3\times5^3). Step 3: 10 is composite, so write 2 and 5 in the final prime form.
View question detailsWhat is the correct prime factorisation of 1024?
Correct answer: A
Step 1: Divide 1024 repeatedly by 2. Step 2: Ten factors of 2 give (1024=2^{10}). Step 3: 4 and 32 are composite, so write the power of 2 in final prime form.
View question detailsWhich is the 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: 105 is composite, so break it further.
View question detailsWhat is the correct 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: Write both 24 and 49 in prime form.
View question detailsWhich is the 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: 35 is composite, so write prime bases 5 and 7.
View question detailsWhat is the correct 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: Convert 16 and 81 into prime powers.
View question detailsWhich is the 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: Do not leave 27 and 49 in the final form.
View question detailsWhat is the correct 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, so count it carefully.
View question detailsWhich is the prime factorisation of 1575?
Correct answer: A
Step 1: Write (1575=225\times7). Step 2: (225=3^2\times5^2), so (1575=3^2\times5^2\times7). Step 3: Convert 225 into prime powers.
View question detailsWhat is the correct 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: 12 is composite, so write powers of 2 and 3 in the final prime form.
View question detailsWhich is the prime factorisation of 1764?
Correct answer: A
Step 1: (1764=42^2). Step 2: Since (42=2\times3\times7), (1764=2^2\times3^2\times7^2). Step 3: In a square number, each prime power should be even.
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