Which number has prime factorisation (2^4\times3^4\times11)?
Correct answer: A
Step 1: Calculate (2^4=16) and (3^4=81). Step 2: (16\times81\times11=14256). Step 3: Solve powers first, then multiply by 11.
Mathematics
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.
TOPIC PRACTICE
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Hard · Level 6
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- 14256
- 7128
- 28512
- 18144
Hard · Level 6
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- 18144
- 9072
- 36288
- 12096
Hard · Level 6
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- 25410
- 12705
- 50820
- 27720
Hard · Level 6
View options
- 43200
- 21600
- 86400
- 32400
Hard · Level 6
View options
- 127008
- 63504
- 254016
- 95256
Hard · Level 6
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- 21
- 3
- 7
- 35
Hard · Level 6
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- (2\times5)
- (2^2\times5)
- (2\times5^2)
- (5\times11)
Hard · Level 6
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- (2\times3^2\times5^2\times13)
- (2\times3\times5\times13)
- (2^2\times3^2\times5\times13)
- (3^2\times5^2)
Hard · Level 6
View options
- (2\times3^2\times5^2\times7)
- (2^2\times3\times5\times7)
- (2\times3\times5^2\times7^2)
- (3^2\times5\times7)
Hard · Level 6
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- (11^3)
- (2^7\times3^5)
- (3^6\times5^3)
- (2^8\times11^2)
Hard · Level 6
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- (2^9\times3^4\times7^3\times13)
- (2^{11}\times3^4)
- (3^6\times7^2)
- (2^{10}\times13^3)
Hard · Level 6
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- 25
- 5
- 20
- 27
Hard · Level 6
View options
- 5
- 20
- 6
- 4
Hard · Level 6
View options
- 9
- 5
- 4
- 8
Hard · Level 6
View options
- 4
- 3
- 1
- 5
Hard · Level 6
View options
- 127008
- 63504
- 254016
- 95256
Hard · Level 6
View options
- 95256
- 47628
- 190512
- 68040
Hard · Level 6
View options
- (2^3\times3^3\times5\times7^2)
- (8\times135\times49)
- (2^3\times27\times245)
- (216\times245)
Hard · Level 6
View options
- (2^5\times81\times49)
- (2^5\times3^4\times7^2)
- (2^6\times3^3\times5^2)
- (2\times5\times7\times11^3)
Hard · Level 6
View options
- 43200
- 21600
- 86400
- 32400
Hard · Level 6
View options
- 108900
- 54450
- 217800
- 27225
Hard · Level 6
View options
- (2^3\times3^4\times5\times7^2)
- (2^4\times3^3\times5\times7^2)
- (8\times19845)
- (2^3\times405\times49)
Hard · Level 6
View options
- (2^3\times3^2\times5^2\times11^2)
- (2^2\times3^3\times5^2\times11^2)
- (8\times27225)
- (2^3\times225\times121)
Hard · Level 6
View options
- (2^7\times3^7)
- (2^6\times3^7)
- (128\times2187)
- (6^7)
Hard · Level 6
View options
- Because 8 and 27225 are composite forms
- Because 8 is prime
- Because 27225 cannot be factorised
- Because the product will change
Which number has prime factorisation (2^5\times3^4\times7)?
Correct answer: A
Step 1: Calculate (2^5=32) and (3^4=81). Step 2: (32\times81\times7=18144). Step 3: It is better to find higher powers first.
Which number has prime factorisation (2\times3\times5\times7\times11^2)?
Correct answer: A
Step 1: Calculate (11^2=121). Step 2: (2\times3\times5\times7\times121=25410). Step 3: First take the product of smaller factors as 210, then multiply by 121.
Which number has prime factorisation (2^6\times3^3\times5^2)?
Correct answer: A
Step 1: Calculate (2^6=64), (3^3=27), and (5^2=25). Step 2: (64\times27\times25=43200). Step 3: Simplify all three powers separately.
Which number has prime factorisation (2^5\times3^4\times7^2)?
Correct answer: A
Step 1: Calculate (2^5=32), (3^4=81), and (7^2=49). Step 2: (32\times81\times49=127008). Step 3: Solving powers first keeps multiplication clear.
If the number is (2^8\times3^5\times5^2\times7^3), by which smallest number should it be multiplied to make a perfect square?
Correct answer: A
Step 1: In a perfect square, all exponents should be even. Step 2: The powers of 3 and 7 are odd. Step 3: Multiplying by (3\times7=21) makes both powers even.
If the number is (2^9\times3^4\times5^7\times11^2), by which smallest number should it be divided to make a perfect square?
Correct answer: A
Step 1: For a perfect square, exponents should be even. Step 2: The powers of 2 and 5 are odd. Step 3: Dividing by (2\times5) makes the powers 8 and 6.
If the number is (2^5\times3^7\times5^4\times13^2), by which smallest number should it be multiplied to make a perfect cube?
Correct answer: A
Step 1: In a perfect cube, every exponent must be a multiple of 3. Step 2: Powers 5, 7, 4, and 2 must become 6, 9, 6, and 3. Step 3: The smallest multiplier is (2\times3^2\times5^2\times13).
If the number is (2^{10}\times3^8\times5^5\times7^4), by which smallest number should it be divided to make a perfect cube?
Correct answer: A
Step 1: For a perfect cube, exponents should be multiples of 3. Step 2: Reducing 10 to 9, 8 to 6, 5 to 3, and 4 to 3 is the smallest way. Step 3: Therefore, the divisor is (2\times3^2\times5^2\times7).
If (n=2^8\times3^6\times5^4\times11^2), by which number will (n) not be divisible?
Correct answer: A
Step 1: Every prime power of a divisor must be available in the number. Step 2: (n) has power 2 of 11, but (11^3) needs power 3. Step 3: Therefore, (n) is not divisible by (11^3).
If (n=2^{10}\times3^5\times7^4\times13^2), by which number must (n) be divisible?
Correct answer: A
Step 1: For divisibility, exponents in the divisor must not exceed those in the given number. Step 2: (2^9), (3^4), (7^3), and 13 are all available in (n). Step 3: Therefore, (n) must be divisible by the first option.
If a number has prime factorisation (2^9\times3^7\times5^4\times7^3\times11^2), how many prime factors does it have with repetition?
Correct answer: A
Step 1: To count with repetition, add the exponents. Step 2: (9+7+4+3+2=25). Step 3: Keep the number of bases and the total count with repetition separate.
If a number has prime factorisation (2^6\times3^5\times7^4\times11^3\times13^2), how many distinct prime factors does it have?
Correct answer: A
Step 1: While counting distinct primes, only bases are counted. Step 2: The bases are 2, 3, 7, 11, and 13. Step 3: Therefore, the number of distinct prime factors is 5.
If (a=2^6\times3^4\times5^2\times11) and (b=2^3\times3^5\times7\times11^2), what will be the power of 3 in (ab)?
Correct answer: A
Step 1: In multiplication, powers of the same prime base are added. Step 2: The power of 3 in (a) is 4 and in (b) is 5. Step 3: In (ab), the power of 3 will be (4+5=9).
If (x=2^8\times5^3\times7^2\times13) and (y=2^5\times3^2\times5^4\times13^3), what will be the power of 13 in (xy)?
Correct answer: A
Step 1: Powers with the same base 13 are added in multiplication. Step 2: The power of 13 in (x) is 1 and in (y) is 3. Step 3: The total power will be (1+3=4).
Which option gives the correct value of (2^5\times3^4\times7^2)?
Correct answer: A
Step 1: Calculate (2^5=32), (3^4=81), and (7^2=49). Step 2: (32\times81\times49=127008). Step 3: Solve all three powers separately first.
Which option gives the correct value of (2^3\times3^5\times7^2)?
Correct answer: A
Step 1: Calculate (2^3=8), (3^5=243), and (7^2=49). Step 2: (8\times243\times49=95256). Step 3: Simplify higher powers first.
Which option gives only the final prime factorisation?
Correct answer: A
Step 1: In the final form, every base must be prime. Step 2: In the first option, bases 2, 3, 5, and 7 are prime. Step 3: 8, 135, 49, 27, 245, and 216 are composite, so they are not final forms.
Which option has incomplete prime factorisation?
Correct answer: A
Step 1: In an incomplete form, composite bases remain. Step 2: 81 and 49 are composite bases. Step 3: (2^5\times81\times49) must be changed into (2^5\times3^4\times7^2).
If (2^6\times3^3\times5^2) is the prime factorisation of a number, what is the number?
Correct answer: A
Step 1: (2^6=64), (3^3=27), and (5^2=25). Step 2: (64\times27\times25=43200). Step 3: Solving powers first helps find the correct option quickly.
If (2^2\times3^2\times5^2\times11^2) is the prime factorisation of a number, what is the number?
Correct answer: A
Step 1: Calculate (2^2=4), (3^2=9), (5^2=25), and (11^2=121). Step 2: (4\times9\times25\times121=108900). Step 3: This is a square form, so observe the powers carefully.
What is the correct prime factorisation of 158760?
Correct answer: A
Step 1: Write (158760=8\times19845). Step 2: (19845=3^4\times5\times7^2), so (158760=2^3\times3^4\times5\times7^2). Step 3: Break 19845 completely.
Which is the prime factorisation of 217800?
Correct answer: A
Step 1: Write (217800=8\times27225). Step 2: (27225=3^2\times5^2\times11^2), so (217800=2^3\times3^2\times5^2\times11^2). Step 3: Convert 27225 into prime powers.
What is the correct prime factorisation of 279936?
Correct answer: A
Step 1: (279936) can be written as (128\times2187). Step 2: (128=2^7) and (2187=3^7), so (279936=2^7\times3^7). Step 3: Do not leave 128 and 2187 in the final form.
Why will (8\times27225) not be considered the final answer in prime factorisation?
Correct answer: A
Step 1: In final prime factorisation, every base should be prime. Step 2: (8=2^3) and (27225=3^2\times5^2\times11^2). Step 3: Therefore, the final form is (2^3\times3^2\times5^2\times11^2).
QUIZ COMPLETE