Which number has prime factorisation 3 × 5^2?
Answer and explanation
Correct answer: 75
The governing concept is that a prime factorisation represents a number as the product of its prime factors, including the indicated powers. Evaluate the power first: 5^2 = 5 × 5 = 25. Now multiply by 3: 3 × 25 = 75. Therefore, option A is correct. The result can be checked by writing 75 as 3 × 25 = 3 × 5^2, so no prime factor is missing or added. Option B, 45, equals 3^2 × 5, which has different exponents. Options C and D are divisible by 2 and therefore contain an extra prime factor not present in the stated factorisation.
Frequently asked questions
What is the correct answer to this question?
75
Why is this the correct answer?
The governing concept is that a prime factorisation represents a number as the product of its prime factors, including the indicated powers. Evaluate the power first: 5^2 = 5 × 5 = 25. Now multiply by 3: 3 × 25 = 75. Therefore, option A is correct. The result can be checked by writing 75 as 3 × 25 = 3 × 5^2, so no prime factor is missing or added. Option B, 45, equals 3^2 × 5, which has different exponents. Options C and D are divisible by 2 and therefore contain an extra prime factor not present in the stated factorisation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Prime Factorisation.
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