Which is the prime factorisation of 100?
Correct answer: A
Step 1: Write (100=4\times25). Step 2: (4=2^2) and (25=5^2), so (100=2^2\times5^2). Step 3: Convert 4 and 25 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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Easy · Level 7 · prime-factorisation,number-100,easy
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- (2^2\times5^2)
- (10\times10)
- (4\times25)
- (2\times50)
Easy · Level 7 · prime-factorisation,number-108,easy
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- (2^2\times3^3)
- (4\times27)
- (2^3\times3^2)
- (12\times9)
Easy · Level 7 · prime-factorisation,number-120,easy
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- (2^3\times3\times5)
- (12\times10)
- (2^2\times3\times10)
- (5\times24)
Easy · Level 7 · prime-factorisation,number-125,easy
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- (5^3)
- (25\times5)
- (5^2)
- (125\times1)
Easy · Level 7 · prime-factorisation,number-144,easy
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- (2^4\times3^2)
- (12\times12)
- (2^3\times3^3)
- (16\times9)
Easy · Level 7 · exponent-comparison,prime-factorisation,easy
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- 3
- 2
- 4
- 1
Easy · Level 7 · exponent-comparison,prime-factorisation,easy
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- 2
- 1
- 3
- 4
Easy · Level 7 · evaluate-factorisation,number-60,easy
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- 60
- 30
- 90
- 120
Easy · Level 7 · evaluate-factorisation,number-72,easy
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- 72
- 48
- 54
- 96
Easy · Level 7 · evaluate-factorisation,powers,easy
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- 40
- 30
- 20
- 50
Easy · Level 7 · evaluate-factorisation,powers,easy
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- 63
- 42
- 72
- 84
Easy · Level 7 · prime-factors,concept-check,easy
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- (2\times3\times5)
- (4\times3\times5)
- (2\times6\times5)
- (10\times3)
Easy · Level 7 · prime-factorisation,not-final-form,easy
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- (4\times3\times5)
- (2^2\times3\times5)
- (2\times3\times7)
- (3^2\times5)
Easy · Level 7 · prime-factorisation,power-of-two,easy
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- (2^6)
- (2^5)
- (4^3)
- (8^2)
Easy · Level 7 · prime-factorisation,power-of-three,easy
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- (3^4)
- (3^3)
- (9^2)
- (27\times3)
Easy · Level 7 · prime-factorisation,square-number,easy
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- (11^2)
- (11\times12)
- (121\times1)
- (7\times17)
Easy · Level 7 · prime-factorisation,square-number,easy
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- (7^2)
- (7\times6)
- (49\times1)
- (5\times9)
Easy · Level 7 · prime-factorisation,cube-number,easy
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- (3^3)
- (3^2)
- (9\times3)
- (27\times1)
Easy · Level 7 · prime-factorisation,power-of-two,easy
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- (2^5)
- (2^4)
- (4^2)
- (8\times4)
Easy · Level 7 · prime-factorisation,power-of-two,easy
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- (2^4)
- (4^2)
- (2^3)
- (8\times2)
What is the correct prime factorisation of 108?
Correct answer: A
Step 1: Write (108=4\times27). Step 2: (4=2^2) and (27=3^3), so (108=2^2\times3^3). Step 3: Do not forget to change 27 into (3^3).
View question detailsWhich is the prime factorisation of 120?
Correct answer: A
Step 1: Write (120=12\times10). Step 2: (12=2^2\times3) and (10=2\times5), so (120=2^3\times3\times5). Step 3: Count the total number of 2s carefully.
View question detailsWhat is the correct prime factorisation of 125?
Correct answer: A
Step 1: Divide 125 by 5 to get 25. Step 2: (25=5^2), so (125=5^3). Step 3: 25 is composite, so the final form is (5^3).
View question detailsWhich is the prime factorisation of 144?
Correct answer: A
Step 1: Write (144=16\times9). Step 2: (16=2^4) and (9=3^2), so (144=2^4\times3^2). Step 3: Perfect square numbers can have even exponents, so check the powers.
View question detailsIf (72=2^a\times3^2), what is the value of (a)?
Correct answer: A
Step 1: The prime factorisation of 72 is (2^3\times3^2). Step 2: Comparing with the given form, the power of 2 is (a). Step 3: Therefore, (a=3).
View question detailsIf (90=2\times3^b\times5), what is the value of (b)?
Correct answer: A
Step 1: The prime factorisation of 90 is (2\times3^2\times5). Step 2: In the given form, the power of 3 is (b). Step 3: Comparing gives (b=2).
View question detailsWhich number has prime factorisation (2^2\times3\times5)?
Correct answer: A
Step 1: Calculate (2^2=4). Step 2: (4\times3\times5=60). Step 3: To get the number from prime factorisation, multiply all factors.
View question detailsWhich number has prime factorisation (2^3\times3^2)?
Correct answer: A
Step 1: Calculate (2^3=8) and (3^2=9). Step 2: (8\times9=72). Step 3: Evaluating powers first gives the answer quickly.
View question detailsIf (n=2^3\times5), what is the value of (n)?
Correct answer: A
Step 1: (2^3=8). Step 2: (8\times5=40). Step 3: Multiply the factors to convert prime factorisation into the number.
View question detailsIf (m=3^2\times7), what is the value of (m)?
Correct answer: A
Step 1: (3^2=9). Step 2: (9\times7=63). Step 3: In an expression with powers, evaluate the power first.
View question detailsWhich option contains only prime factors?
Correct answer: A
Step 1: In prime factorisation, every factor must be prime. Step 2: 2, 3, and 5 are prime. Step 3: 4, 6, and 10 are composite, so they cannot remain in the final prime form.
View question detailsWhich option is not a final prime factorisation?
Correct answer: A
Step 1: A final prime factorisation must not contain a composite number. Step 2: 4 is composite, so (4\times3\times5) is not final form. Step 3: Change 4 into (2^2).
View question detailsWhat is the prime factorisation of 64?
Correct answer: A
Step 1: Divide 64 repeatedly by 2. Step 2: Six factors of 2 give (64=2^6). Step 3: 4 and 8 are composite, so do not write them in final prime form.
View question detailsWhat is the prime factorisation of 81?
Correct answer: A
Step 1: Divide 81 repeatedly by 3. Step 2: Four factors of 3 give (81=3^4). Step 3: 9 and 27 are composite, so write the power of 3 in final prime form.
View question detailsWhat is the prime factorisation of 121?
Correct answer: A
Step 1: 121 is a square number. Step 2: (121=11\times11=11^2). Step 3: Since 11 is prime, (11^2) is the correct prime factorisation.
View question detailsWhich is the prime factorisation of 49?
Correct answer: A
Step 1: 49 can be written as (7\times7). Step 2: Since 7 is prime, (49=7^2). Step 3: In a square number, the same prime may appear twice.
View question detailsWhat is the prime factorisation of 27?
Correct answer: A
Step 1: Write 27 as (3\times9). Step 2: Since (9=3^2), (27=3^3). Step 3: 9 is composite, so the final form is (3^3).
View question detailsWhich is the prime factorisation of 32?
Correct answer: A
Step 1: Divide 32 repeatedly by 2. Step 2: Five factors of 2 give (32=2^5). Step 3: 4 and 8 are composite, so do not write them in final form.
View question detailsWhat is the prime factorisation of 16?
Correct answer: A
Step 1: 16 is (2\times2\times2\times2). Step 2: Therefore, (16=2^4). Step 3: 4 and 8 are composite, so write the power of 2 in final prime form.
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