Which is the prime factorisation of 8820?
Correct answer: A
Step 1: Write (8820=180\times49). Step 2: (180=2^2\times3^2\times5) and (49=7^2), so (8820=2^2\times3^2\times5\times7^2). Step 3: Convert 180 and 49 into prime powers.
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 7 · prime-factorisation,number-8820,hard
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- (2^2\times3^2\times5\times7^2)
- (2\times3^2\times5\times7^2)
- (180\times49)
- (4\times2205)
Hard · Level 7 · prime-factorisation,number-9800,hard
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- (2^3\times5^2\times7^2)
- (2^2\times5^2\times7^2)
- (8\times1225)
- (2^3\times35^2)
Hard · Level 7 · prime-factorisation,number-10368,hard
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- (2^7\times3^4)
- (2^6\times3^4)
- (128\times81)
- (2^7\times27\times3)
Hard · Level 7 · prime-factorisation,number-12320,hard
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- (2^5\times5\times7\times11)
- (2^4\times5\times7\times11)
- (32\times385)
- (2^5\times35\times11)
Hard · Level 7 · prime-factorisation,number-13230,hard
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- (2\times3^3\times5\times7^2)
- (2^2\times3^2\times5\times7^2)
- (270\times49)
- (2\times135\times49)
Hard · Level 7 · prime-factorisation,number-14700,hard
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- (2^2\times3\times5^2\times7^2)
- (2\times3^2\times5^2\times7^2)
- (300\times49)
- (4\times3675)
Hard · Level 7 · prime-factorisation,number-15840,hard
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- (2^5\times3^2\times5\times11)
- (2^4\times3^2\times5\times11)
- (32\times495)
- (2^5\times45\times11)
Hard · Level 7 · prime-factorisation,number-17640,hard
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- (2^3\times3^2\times5\times7^2)
- (2^4\times3^2\times5\times7)
- (8\times2205)
- (2^3\times45\times49)
Hard · Level 7 · prime-factorisation,square-number,hard
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- (2^8\times3^4)
- (2^7\times3^4)
- (256\times81)
- (144^2)
Hard · Level 7 · prime-factorisation,number-22050,hard
View options
- (2\times3^2\times5^2\times7^2)
- (2^2\times3\times5^2\times7^2)
- (450\times49)
- (2\times225\times49)
Hard · Level 7 · prime-factorisation,number-27720,hard
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- (2^3\times3^2\times5\times7\times11)
- (2^2\times3^3\times5\times7\times11)
- (8\times3465)
- (2^3\times9\times385)
Hard · Level 7 · exponent-comparison,number-15840,hard
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- 5
- 4
- 6
- 3
Hard · Level 7 · exponent-comparison,number-22050,hard
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- 2
- 1
- 3
- 4
Hard · Level 7 · exponent-comparison,number-20736,hard
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- 8
- 7
- 6
- 9
Hard · Level 7 · distinct-prime-factors,prime-exponents,hard
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- 5
- 8
- 6
- 11
Hard · Level 7 · evaluate-factorisation,number-2376,hard
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- 2376
- 1188
- 4752
- 3564
Hard · Level 7 · evaluate-factorisation,number-3465,hard
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- 3465
- 1732
- 6930
- 1155
Hard · Level 7 · evaluate-factorisation,number-5040,hard
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- 5040
- 2520
- 10080
- 7560
Hard · Level 7 · evaluate-factorisation,number-5292,hard
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- 5292
- 2646
- 10584
- 4410
Hard · Level 7 · evaluate-factorisation,number-10368,hard
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- 10368
- 5184
- 20736
- 7776
What is the correct prime factorisation of 9800?
Correct answer: A
Step 1: Write (9800=8\times1225). Step 2: (8=2^3) and (1225=5^2\times7^2), so (9800=2^3\times5^2\times7^2). Step 3: Do not leave 1225 in the final form.
View question detailsWhich is the prime factorisation of 10368?
Correct answer: A
Step 1: Write (10368=128\times81). Step 2: (128=2^7) and (81=3^4), so (10368=2^7\times3^4). Step 3: Write both 128 and 81 as prime powers.
View question detailsWhat is the correct prime factorisation of 12320?
Correct answer: A
Step 1: Write (12320=32\times385). Step 2: (32=2^5) and (385=5\times7\times11), so (12320=2^5\times5\times7\times11). Step 3: Give 385 its complete prime form.
View question detailsWhich is the prime factorisation of 13230?
Correct answer: A
Step 1: Write (13230=270\times49). Step 2: (270=2\times3^3\times5) and (49=7^2), so (13230=2\times3^3\times5\times7^2). Step 3: Do not keep 270 and 49 in the final form.
View question detailsWhat is the correct prime factorisation of 14700?
Correct answer: A
Step 1: Write (14700=300\times49). Step 2: (300=2^2\times3\times5^2) and (49=7^2), so (14700=2^2\times3\times5^2\times7^2). Step 3: Convert 300 into prime powers.
View question detailsWhich is the prime factorisation of 15840?
Correct answer: A
Step 1: Write (15840=32\times495). Step 2: (32=2^5) and (495=3^2\times5\times11), so (15840=2^5\times3^2\times5\times11). Step 3: Give 495 its complete prime form.
View question detailsWhat is the correct prime factorisation of 17640?
Correct answer: A
Step 1: Write (17640=8\times2205). Step 2: (2205=3^2\times5\times7^2), so (17640=2^3\times3^2\times5\times7^2). Step 3: Give 2205 its complete prime form.
View question detailsWhich is the prime factorisation of 20736?
Correct answer: A
Step 1: Write (20736=256\times81). Step 2: (256=2^8) and (81=3^4), so (20736=2^8\times3^4). Step 3: Convert 256 and 81 into prime powers.
View question detailsWhat is the correct prime factorisation of 22050?
Correct answer: A
Step 1: Write (22050=450\times49). Step 2: (450=2\times3^2\times5^2) and (49=7^2), so (22050=2\times3^2\times5^2\times7^2). Step 3: Give 450 its complete prime form.
View question detailsWhich is the prime factorisation of 27720?
Correct answer: A
Step 1: Write (27720=8\times3465). Step 2: (3465=3^2\times5\times7\times11), so (27720=2^3\times3^2\times5\times7\times11). Step 3: Give 3465 its complete prime form.
View question detailsIf (15840=2^a\times3^2\times5\times11), what is the value of (a)?
Correct answer: A
Step 1: (15840=32\times495). Step 2: (32=2^5) and (495=3^2\times5\times11), so the power of 2 is 5. Step 3: Comparing gives (a=5).
View question detailsIf (22050=2\times3^b\times5^2\times7^2), what is the value of (b)?
Correct answer: A
Step 1: Write (22050=450\times49). Step 2: (450=2\times3^2\times5^2) and (49=7^2), so the power of 3 is 2. Step 3: Comparing with the given form gives (b=2).
View question detailsIf (20736=2^m\times3^4), what is the value of (m)?
Correct answer: A
Step 1: (20736) can be written as (256\times81). Step 2: (256=2^8) and (81=3^4), so (20736=2^8\times3^4). Step 3: Comparing gives (m=8).
View question detailsIf (27720=2^3\times3^2\times5\times7\times11), how many distinct prime factors does it have?
Correct answer: A
Step 1: For distinct prime factors, exponents are not added. Step 2: The bases are 2, 3, 5, 7, and 11. Step 3: Therefore, there are 5 distinct prime factors.
View question detailsWhich number has prime factorisation (2^3\times3^3\times11)?
Correct answer: A
Step 1: Calculate (2^3=8) and (3^3=27). Step 2: (8\times27\times11=2376). Step 3: Finding powers first is the correct method.
View question detailsWhich number has prime factorisation (3^2\times5\times7\times11)?
Correct answer: A
Step 1: Calculate (3^2=9). Step 2: (9\times5\times7\times11=3465). Step 3: When there are many factors, multiply in pairs.
View question detailsWhich number has prime factorisation (2^4\times3^2\times5\times7)?
Correct answer: A
Step 1: Calculate (2^4=16) and (3^2=9). Step 2: (16\times9\times5\times7=5040). Step 3: First do (16\times9=144), then multiply the rest.
View question detailsWhich number has prime factorisation (2^2\times3^3\times7^2)?
Correct answer: A
Step 1: Calculate (2^2=4), (3^3=27), and (7^2=49). Step 2: (4\times27\times49=5292). Step 3: Simplify all three powers separately.
View question detailsWhich number has prime factorisation (2^7\times3^4)?
Correct answer: A
Step 1: Calculate (2^7=128) and (3^4=81). Step 2: (128\times81=10368). Step 3: Solving large powers first reduces mistakes.
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