Which option gives the correct value of (2^4\times3^3\times7^2)?
Correct answer: A
Step 1: Calculate (2^4=16), (3^3=27), and (7^2=49). Step 2: (16\times27\times49=21168). Step 3: Solve all three powers separately first.
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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Hard · Level 8 · evaluate-factorisation,number-21168,hard
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- 21168
- 10584
- 28224
- 14112
Hard · Level 8 · evaluate-factorisation,number-28224,hard
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- 28224
- 14112
- 56448
- 21168
Hard · Level 8 · prime-factorisation,final-form,hard
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- (2^4\times3^2\times5\times7^2)
- (16\times45\times49)
- (2^4\times45\times49)
- (8\times4410)
Hard · Level 8 · prime-factorisation,incomplete-form,hard
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- (2^5\times21^2)
- (2^5\times3^2\times7^2)
- (2^3\times3^2\times5\times7\times11)
- (3^2\times5^2\times7^2)
Hard · Level 8 · evaluate-factorisation,hard,mcq
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- 28224
- 14112
- 56448
- 21168
Hard · Level 8 · evaluate-factorisation,square-number,hard
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- 19600
- 9800
- 39200
- 4900
Hard · Level 8 · prime-factorisation,number-39200,hard
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- (2^5\times5^2\times7^2)
- (2^4\times5^2\times7^2)
- (32\times1225)
- (2^5\times35^2)
Hard · Level 8 · prime-factorisation,number-41580,hard
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- (2^2\times3^3\times5\times7\times11)
- (2\times3^3\times5\times7\times11)
- (4\times10395)
- (36\times1155)
Hard · Level 8 · prime-factorisation,number-62208,hard
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- (2^8\times3^5)
- (2^7\times3^5)
- (256\times243)
- (2^8\times81\times3)
Hard · Level 8 · prime-factorisation,concept-check,hard
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- Because 8 and 3465 are composite forms
- Because 8 is prime
- Because 3465 cannot be factorised
- Because the product changes
Hard · Level 7 · prime-factorisation,composite-base,hard
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- Because 18 is composite
- Because 5 is composite
- Because powers cannot be used
- Because the product changes
Hard · Level 7 · prime-factorisation,number-2376,hard
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- (2^3\times3^3\times11)
- (2^2\times3^3\times11)
- (8\times297)
- (2^3\times27\times11)
Hard · Level 7 · prime-factorisation,number-3465,hard
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- (3^2\times5\times7\times11)
- (3\times5\times7\times11)
- (9\times385)
- (45\times77)
Hard · Level 7 · prime-factorisation,number-4410,hard
View options
- (2\times3^2\times5\times7^2)
- (2^2\times3\times5\times7^2)
- (90\times49)
- (2\times45\times49)
Hard · Level 7 · prime-factorisation,number-5040,hard
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- (2^4\times3^2\times5\times7)
- (2^3\times3^2\times5\times7)
- (16\times315)
- (2^4\times9\times35)
Hard · Level 7 · prime-factorisation,number-5292,hard
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- (2^2\times3^3\times7^2)
- (2^3\times3^2\times7^2)
- (4\times1323)
- (12\times441)
Hard · Level 7 · prime-factorisation,number-5670,hard
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- (2\times3^4\times5\times7)
- (2\times3^3\times5\times7)
- (81\times70)
- (2\times81\times35)
Hard · Level 7 · prime-factorisation,number-7350,hard
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- (2\times3\times5^2\times7^2)
- (2^2\times3\times5\times7^2)
- (150\times49)
- (2\times75\times49)
Hard · Level 7 · prime-factorisation,number-7560,hard
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- (2^3\times3^3\times5\times7)
- (2^2\times3^3\times5\times7)
- (8\times945)
- (2^3\times27\times35)
Hard · Level 7 · prime-factorisation,number-8085,hard
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- (3\times5\times7^2\times11)
- (3^2\times5\times7\times11)
- (15\times539)
- (3\times2695)
Which option gives the correct value of (2^6\times3^2\times7^2)?
Correct answer: A
Step 1: Calculate (2^6=64), (3^2=9), and (7^2=49). Step 2: (64\times9\times49=28224). Step 3: Do multiplication step by step to avoid mistakes.
View question detailsWhich option gives only the final prime factorisation?
Correct answer: A
Step 1: In the final form, bases must be prime. Step 2: In the first option, bases 2, 3, 5, and 7 are prime. Step 3: 16, 45, 49, and 4410 are composite, so they are not final forms.
View question detailsWhich option has incomplete prime factorisation?
Correct answer: A
Step 1: In an incomplete form, a composite base remains. Step 2: 21 is composite and (21=3\times7), so (2^5\times21^2) is not final. Step 3: Change it into (2^5\times3^2\times7^2).
View question detailsIf (2^6\times3^2\times7^2) is the prime factorisation of a number, what is the number?
Correct answer: A
Step 1: (2^6=64), (3^2=9), and (7^2=49). Step 2: (64\times9\times49=28224). Step 3: Solving powers first helps find the correct option quickly.
View question detailsIf (2^4\times5^2\times7^2) is the prime factorisation of a number, what is the number?
Correct answer: A
Step 1: Calculate (2^4=16), (5^2=25), and (7^2=49). Step 2: (16\times25\times49=19600). Step 3: Finding all three powers separately is safer.
View question detailsWhat is the correct prime factorisation of 39200?
Correct answer: A
Step 1: Write (39200=32\times1225). Step 2: (32=2^5) and (1225=5^2\times7^2), so (39200=2^5\times5^2\times7^2). Step 3: Convert 1225 into prime powers.
View question detailsWhich is the prime factorisation of 41580?
Correct answer: A
Step 1: Write (41580=4\times10395). Step 2: (10395=3^3\times5\times7\times11), so (41580=2^2\times3^3\times5\times7\times11). Step 3: Give 10395 its complete prime form.
View question detailsWhat is the correct prime factorisation of 62208?
Correct answer: A
Step 1: Write (62208=256\times243). Step 2: (256=2^8) and (243=3^5), so (62208=2^8\times3^5). Step 3: Write 256 and 243 as prime powers.
View question detailsWhy will (8\times3465) not be considered the final answer in prime factorisation?
Correct answer: A
Step 1: In prime factorisation, every final factor should be in prime-base form. Step 2: (8=2^3) and (3465=3^2\times5\times7\times11). Step 3: Therefore, the final form is (2^3\times3^2\times5\times7\times11).
View question detailsWhy is (18^2\times5) not considered the final form in prime factorisation?
Correct answer: A
Step 1: In the final prime factorisation, bases must be prime. Step 2: (18=2\times3^2), so (18^2) must be changed into (2^2\times3^4). Step 3: Do not leave a composite base in the final answer.
View question detailsWhat is the correct prime factorisation of 2376?
Correct answer: A
Step 1: Write (2376=8\times297). Step 2: (8=2^3) and (297=3^3\times11), so (2376=2^3\times3^3\times11). Step 3: Do not leave 297 in the final form.
View question detailsWhich is the prime factorisation of 3465?
Correct answer: A
Step 1: Write (3465=9\times385). Step 2: (9=3^2) and (385=5\times7\times11), so (3465=3^2\times5\times7\times11). Step 3: Give 385 its complete prime form too.
View question detailsWhat is the correct prime factorisation of 4410?
Correct answer: A
Step 1: Write (4410=90\times49). Step 2: (90=2\times3^2\times5) and (49=7^2), so (4410=2\times3^2\times5\times7^2). Step 3: Give prime form to both 90 and 49.
View question detailsWhich is the prime factorisation of 5040?
Correct answer: A
Step 1: Write (5040=16\times315). Step 2: (16=2^4) and (315=3^2\times5\times7), so (5040=2^4\times3^2\times5\times7). Step 3: Give 315 its complete prime form.
View question detailsWhat is the correct prime factorisation of 5292?
Correct answer: A
Step 1: Write (5292=4\times1323). Step 2: (4=2^2) and (1323=3^3\times7^2), so (5292=2^2\times3^3\times7^2). Step 3: Convert 1323 into powers of 3 and 7.
View question detailsWhich is the prime factorisation of 5670?
Correct answer: A
Step 1: Write (5670=81\times70). Step 2: (81=3^4) and (70=2\times5\times7), so (5670=2\times3^4\times5\times7). Step 3: It is necessary to change 81 into (3^4).
View question detailsWhat is the correct prime factorisation of 7350?
Correct answer: A
Step 1: Write (7350=150\times49). Step 2: (150=2\times3\times5^2) and (49=7^2), so (7350=2\times3\times5^2\times7^2). Step 3: Break 150 and 49 completely and separately.
View question detailsWhich is the prime factorisation of 7560?
Correct answer: A
Step 1: Write (7560=8\times945). Step 2: (8=2^3) and (945=3^3\times5\times7), so (7560=2^3\times3^3\times5\times7). Step 3: Do not leave 945 in the final form.
View question detailsWhat is the correct prime factorisation of 8085?
Correct answer: A
Step 1: Write (8085=15\times539). Step 2: (15=3\times5) and (539=7^2\times11), so (8085=3\times5\times7^2\times11). Step 3: Give 539 its complete prime form too.
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