Which number has prime factorisation (2^3\times3^2\times7\times11)?
Correct answer: A
Step 1: Calculate (2^3=8) and (3^2=9). Step 2: (8\times9\times7\times11=5544). Step 3: Simplify powers first and then multiply.
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 2
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- 5544
- 2772
- 11088
- 8316
Hard · Level 2
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- 6048
- 3024
- 12096
- 8064
Hard · Level 2
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- 11025
- 3675
- 22050
- 1225
Hard · Level 2
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- 11760
- 5880
- 23520
- 17640
Hard · Level 2
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- 31104
- 15552
- 62208
- 20736
Hard · Level 2
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- 14
- 7
- 2
- 28
Hard · Level 2
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- 3
- 9
- 15
- 5
Hard · Level 2
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- 588
- 147
- 84
- 441
Hard · Level 2
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- (2^2\times3^2\times5\times11^2)
- (2\times3\times5^2\times11)
- (2^2\times3\times5\times11)
- (3^2\times5^2\times11^2)
Hard · Level 2
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- (3^5)
- (2^5\times3^4)
- (2^6\times5^2\times7)
- (3^2\times5\times7)
Hard · Level 2
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- (2^7\times3^2\times5^4)
- (2^9\times3^2)
- (3^4\times5)
- (2^8\times5^6)
Hard · Level 2
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- 10
- 4
- 8
- 12
Hard · Level 2
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- 4
- 15
- 7
- 5
Hard · Level 2
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- 6
- 4
- 2
- 8
Hard · Level 2
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- 8
- 5
- 3
- 10
Hard · Level 2
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- 21168
- 10584
- 28224
- 14112
Hard · Level 2
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- 28224
- 14112
- 56448
- 21168
Hard · Level 2
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- (2^4\times3^2\times5\times7^2)
- (16\times45\times49)
- (2^4\times45\times49)
- (8\times4410)
Hard · Level 2
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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 2
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- 28224
- 14112
- 56448
- 21168
Hard · Level 2
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- 19600
- 9800
- 39200
- 4900
Hard · Level 2
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- (2^5\times5^2\times7^2)
- (2^4\times5^2\times7^2)
- (32\times1225)
- (2^5\times35^2)
Hard · Level 2
View options
- (2^2\times3^3\times5\times7\times11)
- (2\times3^3\times5\times7\times11)
- (4\times10395)
- (36\times1155)
Hard · Level 2
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- (2^8\times3^5)
- (2^7\times3^5)
- (256\times243)
- (2^8\times81\times3)
Hard · Level 2
View options
- Because 8 and 3465 are composite forms
- Because 8 is prime
- Because 3465 cannot be factorised
- Because the product changes
Which number has prime factorisation (2^5\times3^3\times7)?
Correct answer: A
Step 1: Calculate (2^5=32) and (3^3=27). Step 2: (32\times27\times7=6048). Step 3: Find the values of higher powers separately.
Which number has prime factorisation (3^2\times5^2\times7^2)?
Correct answer: A
Step 1: Calculate (3^2=9), (5^2=25), and (7^2=49). Step 2: (9\times25\times49=11025). Step 3: In this square form, all exponents are 2, so multiply carefully.
Which number has prime factorisation (2^4\times3\times5\times7^2)?
Correct answer: A
Step 1: Calculate (2^4=16) and (7^2=49). Step 2: (16\times3\times5\times49=11760). Step 3: Calculating powers first makes the work easier.
Which number has prime factorisation (2^7\times3^5)?
Correct answer: A
Step 1: Calculate (2^7=128) and (3^5=243). Step 2: (128\times243=31104). Step 3: Simplifying both powers first is the correct method.
If the number is (2^5\times3^4\times5^2\times7), by which smallest number should it be multiplied to make a perfect square?
Correct answer: A
Step 1: For a perfect square, all exponents must be even. Step 2: The powers of 2 and 7 are odd. Step 3: Multiplying by (2\times7=14) makes all exponents even.
If the number is (2^4\times3^5\times5^2), by which smallest number should it be divided to make a perfect square?
Correct answer: A
Step 1: In a perfect square, all exponents are even. Step 2: Only the power of 3 is odd. Step 3: Dividing by 3 makes the power 4 and the number becomes a perfect square.
If the number is (2^4\times3^2\times5^3\times7), 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 4, 2, and 1 must become 6, 3, and 3 respectively. Step 3: The multiplier is (2^2\times3\times7^2=588).
If the number is (2^8\times3^5\times5^4\times11^2), 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: Reduce 8 to 6, 5 to 3, 4 to 3, and 2 to 0 for the smallest divisor. Step 3: So the divisor is (2^2\times3^2\times5\times11^2).
If (n=2^6\times3^4\times5^2\times7), by which number will (n) not be divisible?
Correct answer: A
Step 1: For divisibility, every prime power of the divisor must be available in the number. Step 2: (n) has power 4 of 3, but (3^5) needs power 5. Step 3: Therefore, (n) is not divisible by (3^5).
If (n=2^8\times3^3\times5^5), by which number must (n) be divisible?
Correct answer: A
Step 1: For divisibility, each exponent in the divisor must be less than or equal to the corresponding exponent in the number. Step 2: (2^7), (3^2), and (5^4) are all available in (n). Step 3: Therefore, (n) must be divisible by (2^7\times3^2\times5^4).
If a number has prime factorisation (2^4\times3^2\times5^2\times7^2), how many prime factors does it have if repetition is counted?
Correct answer: A
Step 1: To count with repetition, add the exponents. Step 2: (4+2+2+2=10). Step 3: Keep the difference between distinct prime count and repeated prime count clear.
If a number has prime factorisation (2^7\times3^5\times11^2\times13), how many distinct prime factors does it have?
Correct answer: A
Step 1: While counting distinct prime factors, do not add exponents. Step 2: The prime bases are 2, 3, 11, and 13. Step 3: Therefore, the number of distinct prime factors is 4.
If (a=2^5\times3^2\times7) and (b=2^3\times3^4\times5), 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 2 and in (b) is 4. Step 3: In (ab), the power of 3 will be (2+4=6).
If (x=2^8\times5^3\times11) and (y=2^4\times3^2\times5^5), what will be the power of 5 in (xy)?
Correct answer: A
Step 1: Powers with the same base 5 are added in multiplication. Step 2: The power of 5 in (x) is 3 and in (y) is 5. Step 3: The total power will be (3+5=8).
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.
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.
Which 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.
Which 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).
If (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.
If (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.
What 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.
Which 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.
What 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.
Why 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).
QUIZ COMPLETE