If (132=2^a\times3\times11), what is the value of (a)?
Correct answer: A
Step 1: The prime factorisation of 132 is (2^2\times3\times11). Step 2: In the given form, the power of 2 is (a). Step 3: Comparing gives (a=2).
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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Easy · Level 4
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- 2
- 1
- 3
- 4
Easy · Level 4
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- 2
- 1
- 3
- 4
Easy · Level 4
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- 168
- 84
- 126
- 336
Easy · Level 4
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- 270
- 180
- 135
- 540
Easy · Level 4
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- 240
- 120
- 180
- 300
Easy · Level 4
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- 315
- 210
- 175
- 420
Easy · Level 4
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- (2\times3\times7\times11)
- (6\times7\times11)
- (21\times11)
- (2\times33\times7)
Easy · Level 4
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- (6\times5^2)
- (2\times3\times5^2)
- (2^2\times3\times7)
- (3^2\times5\times7)
Easy · Level 4
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- (2^8)
- (2^7)
- (4^4)
- (16^2)
Easy · Level 4
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- (3^5)
- (3^4)
- (9^3)
- (27\times9)
Easy · Level 4
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- (13^2)
- (13\times12)
- (169\times1)
- (7\times24)
Easy · Level 4
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- (17^2)
- (17\times18)
- (289\times1)
- (13\times22)
Easy · Level 4
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- (2^9)
- (2^8)
- (8^3)
- (16\times32)
Easy · Level 4
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- (5^4)
- (25^2)
- (5^3)
- (125\times5)
Easy · Level 4
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- (2^3\times3^3)
- (6^3)
- (8\times27)
- (2^4\times3^2)
Easy · Level 4
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- (2^7)
- (2^6)
- (4^3)
- (8\times16)
Easy · Level 4
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- (2^2\times3^3\times5)
- (54\times10)
- (2\times270)
- (6\times90)
Easy · Level 4
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- (2^2\times3\times7^2)
- (12\times49)
- (6\times98)
- (2\times294)
Easy · Level 4
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- (2^2\times3\times5\times11)
- (66\times10)
- (6\times110)
- (22\times30)
Easy · Level 4
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- 132
- 66
- 264
- 99
Easy · Level 4
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- 225
- 150
- 300
- 450
Easy · Level 4
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- 210
- 105
- 420
- 315
Easy · Level 4
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- 252
- 126
- 504
- 378
Easy · Level 4
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- 400
- 200
- 800
- 100
Easy · Level 4
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- Because 1 is not a prime number
- Because 1 is the largest number
- Because 1 is always even
- Because 1 is divisible only by 2
If (150=2\times3\times5^b), what is the value of (b)?
Correct answer: A
Step 1: The prime factorisation of 150 is (2\times3\times5^2). Step 2: In the given form, the power of 5 is (b). Step 3: Comparing gives (b=2).
Which number has prime factorisation (2^3\times3\times7)?
Correct answer: A
Step 1: Calculate (2^3=8). Step 2: (8\times3\times7=168). Step 3: To get the number from prime factorisation, multiply all factors.
Which number has prime factorisation (2\times3^3\times5)?
Correct answer: A
Step 1: Calculate (3^3=27). Step 2: (2\times27\times5=270). Step 3: Evaluating the power first makes calculation easy.
If (n=2^4\times3\times5), what is the value of (n)?
Correct answer: A
Step 1: (2^4=16). Step 2: (16\times3\times5=240). Step 3: Multiply to get the number from prime form.
If (m=3^2\times5\times7), what is the value of (m)?
Correct answer: A
Step 1: Calculate (3^2=9). Step 2: (9\times5\times7=315). Step 3: Simplify the factor with a power first.
Which option contains only prime factors?
Correct answer: A
Step 1: In final prime factorisation, every factor must be prime. Step 2: 2, 3, 7, and 11 are all prime. Step 3: 6, 21, and 33 are composite, so they cannot remain in final form.
Which option is not a final prime factorisation?
Correct answer: A
Step 1: Final prime factorisation must not contain a composite factor. Step 2: 6 is composite, so (6\times5^2) is not final form. Step 3: Change 6 into (2\times3).
What is the prime factorisation of 256?
Correct answer: A
Step 1: Divide 256 repeatedly by 2. Step 2: Eight factors of 2 give (256=2^8). Step 3: 4 and 16 are composite, so do not write them in final prime form.
What is the prime factorisation of 243?
Correct answer: A
Step 1: Divide 243 repeatedly by 3. Step 2: Five factors of 3 give (243=3^5). Step 3: 9 and 27 are composite, so keep prime base 3.
What is the prime factorisation of 169?
Correct answer: A
Step 1: 169 is a square number. Step 2: (169=13\times13=13^2). Step 3: Since 13 is prime, (13^2) is the correct prime factorisation.
Which is the prime factorisation of 289?
Correct answer: A
Step 1: (289=17\times17). Step 2: Since 17 is prime, (289=17^2). Step 3: In a square number, the same prime appears twice.
What is the prime factorisation of 512?
Correct answer: A
Step 1: Divide 512 repeatedly by 2. Step 2: Nine factors of 2 give (512=2^9). Step 3: 8, 16, and 32 are composite, so write the power of 2 in final prime form.
Which is the prime factorisation of 625?
Correct answer: A
Step 1: (625) can be written as (25\times25). Step 2: (25=5^2), so (625=5^4). Step 3: 25 is composite, so write the power of 5 in final form.
What is the prime factorisation of 216?
Correct answer: A
Step 1: Write (216=8\times27). Step 2: (8=2^3) and (27=3^3), so (216=2^3\times3^3). Step 3: 6, 8, and 27 are composite, so write prime bases in final form.
What is the prime factorisation of 128?
Correct answer: A
Step 1: Divide 128 repeatedly by 2. Step 2: Seven factors of 2 give (128=2^7). Step 3: 4, 8, and 16 are composite, so write (2^7) in final form.
Which is the prime factorisation of 540?
Correct answer: A
Step 1: Write (540=54\times10). Step 2: (54=2\times3^3) and (10=2\times5), so (540=2^2\times3^3\times5). Step 3: Break 54 completely into prime form.
What is the correct prime factorisation of 588?
Correct answer: A
Step 1: Write (588=12\times49). Step 2: (12=2^2\times3) and (49=7^2), so (588=2^2\times3\times7^2). Step 3: Convert 12 and 49 into prime powers.
Which is the prime factorisation of 660?
Correct answer: A
Step 1: Write (660=66\times10). Step 2: (66=2\times3\times11) and (10=2\times5), so (660=2^2\times3\times5\times11). Step 3: Since 2 appears twice, write (2^2).
If the prime factorisation of a number is (2^2\times3\times11), which number is it?
Correct answer: A
Step 1: Calculate (2^2=4). Step 2: (4\times3\times11=132). Step 3: Multiply all factors to get the number from prime factorisation.
If the prime factorisation of a number is (3^2\times5^2), which number is it?
Correct answer: A
Step 1: Calculate (3^2=9) and (5^2=25). Step 2: (9\times25=225). Step 3: Simplify powers first and then multiply.
Which number has prime factorisation (2\times3\times5\times7)?
Correct answer: A
Step 1: All prime factors are given. Step 2: (2\times3\times5\times7=210). Step 3: When no power is written, each prime is taken once.
Which number has prime factorisation (2^2\times3^2\times7)?
Correct answer: A
Step 1: Calculate (2^2=4) and (3^2=9). Step 2: (4\times9\times7=252). Step 3: Evaluate prime powers and then multiply.
If the prime factorisation of a number is (2^4\times5^2), which number is it?
Correct answer: A
Step 1: Calculate (2^4=16) and (5^2=25). Step 2: (16\times25=400). Step 3: Finding powers first makes the calculation easier.
Why is 1 not written as a final prime factor during prime factorisation?
Correct answer: A
Step 1: A prime number has exactly two factors. Step 2: 1 has only one factor, so 1 is not prime. Step 3: Do not write 1 as a final factor in prime factorisation.
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