What is the prime factorisation of 25?
Correct answer: A
Step 1: 25 is (5\times5). Step 2: Since 5 is prime, (25=5^2). Step 3: If the same prime appears twice, write power 2.
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,square-number,easy
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- (5^2)
- (5\times4)
- (25\times1)
- (3\times8)
Easy · Level 7 · prime-factorisation,number-80,easy
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- (2^4\times5)
- (2^3\times10)
- (16\times5)
- (8\times10)
Easy · Level 7 · prime-factorisation,number-98,easy
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- (2\times7^2)
- (2^2\times7)
- (14\times7)
- (49\times2)
Easy · Level 7 · prime-factorisation,number-105,easy
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- (3\times5\times7)
- (15\times7)
- (21\times5)
- (35\times3)
Easy · Level 7 · evaluate-factorisation,number-36,easy
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- 36
- 24
- 48
- 72
Easy · Level 7 · real-numbers,prime-factorisation,exponents,number-properties
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- 50
- 25
- 40
- 100
Easy · Level 7 · evaluate-factorisation,number-42,easy
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- 42
- 21
- 56
- 84
Easy · Level 7 · evaluate-factorisation,number-75,easy
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- 75
- 45
- 90
- 150
Easy · Level 7 · evaluate-factorisation,number-48,easy
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- 48
- 24
- 64
- 96
Easy · Level 7 · prime-factorisation,concept-check,easy
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- Composite factor
- Prime factor
- Prime factor like 2
- Prime factor like 3
Easy · Level 8 · prime-factorisation,number-132,easy
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- (2^2\times3\times11)
- (4\times33)
- (2\times66)
- (12\times11)
Easy · Level 8 · prime-factorisation,number-150,easy
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- (2\times3\times5^2)
- (15\times10)
- (2\times75)
- (3^2\times5^2)
Easy · Level 8 · prime-factorisation,number-162,easy
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- (2\times3^4)
- (2^2\times3^3)
- (18\times9)
- (6\times27)
Easy · Level 8 · prime-factorisation,number-168,easy
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- (2^3\times3\times7)
- (8\times21)
- (2^2\times42)
- (6\times28)
Easy · Level 8 · prime-factorisation,number-180,easy
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- (2^2\times3^2\times5)
- (18\times10)
- (2\times90)
- (3^2\times20)
Easy · Level 8 · prime-factorisation,square-number,easy
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- (2^2\times7^2)
- (14\times14)
- (4\times49)
- (2\times98)
Easy · Level 8 · prime-factorisation,number-210,easy
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- (2\times3\times5\times7)
- (21\times10)
- (30\times7)
- (14\times15)
Easy · Level 8 · prime-factorisation,square-number,easy
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- (3^2\times5^2)
- (15\times15)
- (9\times25)
- (3\times75)
Easy · Level 8 · prime-factorisation,number-231,easy
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- (3\times7\times11)
- (21\times11)
- (33\times7)
- (3\times77)
Easy · Level 8 · prime-factorisation,number-240,easy
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- (2^4\times3\times5)
- (24\times10)
- (2^3\times30)
- (16\times15)
Which is the prime factorisation of 80?
Correct answer: A
Step 1: Write (80=16\times5). Step 2: Since (16=2^4), (80=2^4\times5). Step 3: 16 is composite, so change it into (2^4).
View question detailsWhat is the correct prime factorisation of 98?
Correct answer: A
Step 1: Write (98=2\times49). Step 2: Since (49=7^2), (98=2\times7^2). Step 3: 49 is composite, so write (7^2) in the final form.
View question detailsWhich is the prime factorisation of 105?
Correct answer: A
Step 1: Write (105=15\times7). Step 2: (15=3\times5), so (105=3\times5\times7). Step 3: 15, 21, and 35 are composite, so do not keep them in the final answer.
View question detailsIf the prime factorisation of a number is (2^2\times3^2), which number is it?
Correct answer: A
Step 1: Calculate (2^2=4) and (3^2=9). Step 2: (4\times9=36). Step 3: Multiply to get the number from prime factorisation.
View question detailsIf the prime factorisation of a number is \(2\times5^2\), what is the number?
Correct answer: A
Prime factorisation lists the prime factors with their powers. Compute the power first: \(5^2=25\). Then multiply by 2: \(2\times25=50\). So the number is 50. Why other options are wrong: 25 lacks the factor 2; 100 equals \(2^2\times5^2\) (an extra factor 2); 40 equals \(2^3\times5\). Exam tip: evaluate powers first or multiply the listed prime factors directly to get the number.
View question detailsWhich number has prime factorisation (2\times3\times7)?
Correct answer: A
Step 1: The prime factors are given. Step 2: (2\times3\times7=42). Step 3: When no power is written, each prime is taken once.
View question detailsWhich number has prime factorisation (3\times5^2)?
Correct answer: A
Step 1: Calculate (5^2=25). Step 2: (3\times25=75). Step 3: Simplify the power first and then multiply.
View question detailsIf the prime factorisation of a number is (2^4\times3), which number is it?
Correct answer: A
Step 1: Calculate (2^4=16). Step 2: (16\times3=48). Step 3: It is easier to find the value of prime powers first.
View question detailsWhile doing prime factorisation, which type of factor should not remain in the final form?
Correct answer: A
Step 1: A final prime factorisation contains only prime numbers. Step 2: A composite factor must be broken further. Step 3: In exams, do not leave factors like 6, 8, or 10 at the end.
View question detailsWhat is the correct prime factorisation of 132?
Correct answer: A
Step 1: Write (132=4\times33). Step 2: (4=2^2) and (33=3\times11), so (132=2^2\times3\times11). Step 3: Do not keep composite factors like 4 and 33 in the final answer.
View question detailsWhich is the prime factorisation of 150?
Correct answer: A
Step 1: Write (150=15\times10). Step 2: (15=3\times5) and (10=2\times5), so (150=2\times3\times5^2). Step 3: When the same prime repeats, write it as a power.
View question detailsWhat is the correct prime factorisation of 162?
Correct answer: A
Step 1: Write (162=2\times81). Step 2: Since (81=3^4), (162=2\times3^4). Step 3: Do not leave 81 in the final form; write (3^4).
View question detailsWhich is the prime factorisation of 168?
Correct answer: A
Step 1: Write (168=8\times21). Step 2: (8=2^3) and (21=3\times7), so (168=2^3\times3\times7). Step 3: 8 and 21 are composite, so break them further.
View question detailsWhat is the correct prime factorisation of 180?
Correct answer: A
Step 1: Write (180=18\times10). Step 2: (18=2\times3^2) and (10=2\times5), so (180=2^2\times3^2\times5). Step 3: Change all composite factors into prime form.
View question detailsWhich is the prime factorisation of 196?
Correct answer: A
Step 1: (196) can be written as (14\times14) or (4\times49). Step 2: Since (14=2\times7), (196=2^2\times7^2). Step 3: In square numbers, exponents are often even, so check them.
View question detailsWhat is the correct prime factorisation of 210?
Correct answer: A
Step 1: Write (210=21\times10). Step 2: (21=3\times7) and (10=2\times5), so (210=2\times3\times5\times7). Step 3: Do not keep 21 or 10 in the final answer.
View question detailsWhich is the prime factorisation of 225?
Correct answer: A
Step 1: Recognise (225=15^2). Step 2: Since (15=3\times5), (225=3^2\times5^2). Step 3: 15 is composite, so write powers of 3 and 5 in the final form.
View question detailsWhat is the correct prime factorisation of 231?
Correct answer: A
Step 1: Write (231=21\times11). Step 2: Since (21=3\times7), (231=3\times7\times11). Step 3: 21 is composite, so do not keep it in the final answer.
View question detailsWhich is the prime factorisation of 240?
Correct answer: A
Step 1: Write (240=16\times15). Step 2: (16=2^4) and (15=3\times5), so (240=2^4\times3\times5). Step 3: It is necessary to change 16 into (2^4).
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