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Number System · Question 71 of 71

Question 71

HardOriginal question

What is the smallest natural number that has exactly 6 factors?

Options for question 71

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. A number with 6 factors has the form p5p^5 or p2×qp^2 \times q (since 6=6×1=3×26 = 6 \times 1 = 3 \times 2).

  2. Smallest p5p^5 is 25=322^5 = 32. Smallest p2×qp^2 \times q is 22×3=122^2 \times 3 = 12.

  3. So the answer is 12 (factors 1, 2, 3, 4, 6, 12).

Worth noting

18=32×218 = 3^2 \times 2 and 20=22×520 = 2^2 \times 5 also have 6 factors, but they are larger; put the bigger power on the smallest prime.

Concept
Building a number from its factor count
Typical time
110 s
Your time
—
The rule this testsFactors and prime numbers
Practise this chapter →

Ten questions from Number System, at your own pace.

Practise this chapter →

Ten questions from Number System, at your own pace.