Which is the prime factorisation of 2268?
Correct answer: A
Step 1: Write (2268=4\times567). Step 2: (4=2^2) and (567=3^4\times7), so (2268=2^2\times3^4\times7). Step 3: Convert 567 into 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 9 · prime-factorisation,number-2268,medium
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- (2^2\times3^4\times7)
- (2^3\times3^3\times7)
- (4\times567)
- (2^2\times81\times7)
Medium · Level 9 · prime-factorisation,number-2340,medium
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- (2^2\times3^2\times5\times13)
- (2\times3^2\times5\times13)
- (234\times10)
- (4\times585)
Medium · Level 9 · prime-factorisation,number-2450,medium
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- (2\times5^2\times7^2)
- (2^2\times5\times7^2)
- (2\times1225)
- (50\times49)
Medium · Level 9 · prime-factorisation,number-2640,medium
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- (2^4\times3\times5\times11)
- (2^3\times3\times5\times11)
- (24\times110)
- (16\times165)
Medium · Level 9 · prime-factorisation,number-2835,medium
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- (3^4\times5\times7)
- (3^3\times5\times7)
- (81\times35)
- (9\times315)
Medium · Level 9 · prime-factorisation,number-3120,medium
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- (2^4\times3\times5\times13)
- (2^3\times3\times5\times13)
- (312\times10)
- (16\times195)
Medium · Level 9 · prime-factorisation,number-3402,medium
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- (2\times3^5\times7)
- (2\times3^4\times7)
- (2\times1701)
- (486\times7)
Medium · Level 9 · prime-factorisation,number-3528,medium
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- (2^3\times3^2\times7^2)
- (2^2\times3^2\times7^2)
- (72\times49)
- (8\times441)
Medium · Level 9 · prime-factorisation,number-3645,medium
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- (3^6\times5)
- (3^5\times5)
- (729\times5)
- (81\times45)
Medium · Level 9 · prime-factorisation,number-3888,medium
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- (2^4\times3^5)
- (2^3\times3^5)
- (16\times243)
- (2^4\times243)
Medium · Level 9 · prime-factorisation,number-3969,medium
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- (3^4\times7^2)
- (3^3\times7^2)
- (81\times49)
- (63\times63)
Medium · Level 9 · exponent-comparison,number-2016,medium
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- 5
- 4
- 6
- 3
Medium · Level 9 · exponent-comparison,number-2205,medium
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- 2
- 1
- 3
- 4
Medium · Level 9 · exponent-comparison,number-2450,medium
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- 2
- 1
- 3
- 4
Medium · Level 9 · exponent-comparison,number-3888,medium
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- 4
- 3
- 5
- 6
Medium · Level 9 · evaluate-factorisation,number-792,medium
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- 792
- 396
- 1188
- 1584
Medium · Level 9 · evaluate-factorisation,number-825,medium
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- 825
- 550
- 1650
- 275
Medium · Level 9 · evaluate-factorisation,number-864,medium
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- 864
- 432
- 1728
- 1296
Medium · Level 9 · evaluate-factorisation,number-924,medium
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- 924
- 462
- 1848
- 1386
Medium · Level 9 · evaluate-factorisation,number-3120,medium
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- 3120
- 1560
- 6240
- 2340
What is the correct prime factorisation of 2340?
Correct answer: A
Step 1: Write (2340=234\times10). Step 2: (234=2\times3^2\times13) and (10=2\times5), so (2340=2^2\times3^2\times5\times13). Step 3: The power of 2 becomes 2.
View question detailsWhich is the prime factorisation of 2450?
Correct answer: A
Step 1: Write (2450=2\times1225). Step 2: (1225=5^2\times7^2), so (2450=2\times5^2\times7^2). Step 3: Convert 1225 into prime powers.
View question detailsWhat is the correct prime factorisation of 2640?
Correct answer: A
Step 1: Write (2640=16\times165). Step 2: (16=2^4) and (165=3\times5\times11), so (2640=2^4\times3\times5\times11). Step 3: Break 165 further.
View question detailsWhich is the prime factorisation of 2835?
Correct answer: A
Step 1: Write (2835=81\times35). Step 2: (81=3^4) and (35=5\times7), so (2835=3^4\times5\times7). Step 3: Change 81 into (3^4).
View question detailsWhat is the correct prime factorisation of 3120?
Correct answer: A
Step 1: Write (3120=16\times195). Step 2: (16=2^4) and (195=3\times5\times13), so (3120=2^4\times3\times5\times13). Step 3: Give 195 its complete prime form.
View question detailsWhich is the prime factorisation of 3402?
Correct answer: A
Step 1: Write (3402=2\times1701). Step 2: (1701=3^5\times7), so (3402=2\times3^5\times7). Step 3: Convert 1701 into prime form using 3 and 7.
View question detailsWhat is the correct prime factorisation of 3528?
Correct answer: A
Step 1: Write (3528=72\times49). Step 2: (72=2^3\times3^2) and (49=7^2), so (3528=2^3\times3^2\times7^2). Step 3: Convert 72 and 49 into prime powers.
View question detailsWhich is the prime factorisation of 3645?
Correct answer: A
Step 1: Write (3645=729\times5). Step 2: Since (729=3^6), (3645=3^6\times5). Step 3: 729 should not be left in the final form.
View question detailsWhat is the correct prime factorisation of 3888?
Correct answer: A
Step 1: Write (3888=16\times243). Step 2: (16=2^4) and (243=3^5), so (3888=2^4\times3^5). Step 3: Change 243 into a power of 3.
View question detailsWhich is the prime factorisation of 3969?
Correct answer: A
Step 1: Write (3969=81\times49). Step 2: (81=3^4) and (49=7^2), so (3969=3^4\times7^2). Step 3: Write both parts as prime powers.
View question detailsIf (2016=2^a\times3^2\times7), what is the value of (a)?
Correct answer: A
Step 1: Write (2016=32\times63). Step 2: (32=2^5) and (63=3^2\times7), so (2016=2^5\times3^2\times7). Step 3: Comparing gives (a=5).
View question detailsIf (2205=3^b\times5\times7^2), what is the value of (b)?
Correct answer: A
Step 1: (2205=45\times49). Step 2: (45=3^2\times5) and (49=7^2), so (2205=3^2\times5\times7^2). Step 3: Comparing gives (b=2).
View question detailsIf (2450=2\times5^m\times7^2), what is the value of (m)?
Correct answer: A
Step 1: (2450=2\times1225). Step 2: (1225=5^2\times7^2), so (2450=2\times5^2\times7^2). Step 3: Comparing with the given form gives (m=2).
View question detailsIf (3888=2^p\times3^5), what is the value of (p)?
Correct answer: A
Step 1: Write (3888=16\times243). Step 2: (16=2^4) and (243=3^5), so the power of 2 is 4. Step 3: Comparing gives (p=4).
View question detailsWhich number has prime factorisation (2^3\times3^2\times11)?
Correct answer: A
Step 1: Calculate (2^3=8) and (3^2=9). Step 2: (8\times9\times11=792). Step 3: First solve the powers, then multiply by 11.
View question detailsWhich number has prime factorisation (3\times5^2\times11)?
Correct answer: A
Step 1: Calculate (5^2=25). Step 2: (3\times25\times11=825). Step 3: It is useful to simplify the power part first.
View question detailsWhich number has prime factorisation (2^5\times3^3)?
Correct answer: A
Step 1: Calculate (2^5=32) and (3^3=27). Step 2: (32\times27=864). Step 3: Simplify both powers separately.
View question detailsWhich number has prime factorisation (2^2\times3\times7\times11)?
Correct answer: A
Step 1: Calculate (2^2=4). Step 2: (4\times3\times7\times11=924). Step 3: With many factors, multiply in pairs.
View question detailsWhich number has prime factorisation (2^4\times3\times5\times13)?
Correct answer: A
Step 1: Calculate (2^4=16). Step 2: (16\times3\times5\times13=3120). Step 3: It is easy to first treat (3\times5\times13) as 195 and multiply.
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