Free Practice Question
PS · Problem Solving
655-705
Divisibility/Multiples/Factors
What is the smallest positive integer x, such that 1,080x is a perfect cube?
Answer Choices
Correct answer marked belowA
6
B
8
C
18
25
Correct
E
45
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Explanation
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Official Explanation
Official
To determine the smallest positive integer x that makes 1,080x a perfect cube, we first factor 1,080. The prime factorization of 1,080 is 2^3 * 3^3 * 5^1. For a number to be a perfect cube, all the exponents in its prime factorization must be multiples of 3. Here, we have: - The exponent of…
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What it tests
Your understanding of divisibility rules, least common multiples, and greatest common factors.
Common trap
Forgetting that 1 is not prime and that every integer divides 0.
Details
Difficulty
655-705
Type
PS
Category