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    Question

    How many divisors does the number 5040

    have?
    A 18 Correct Answer Incorrect Answer
    B 20 Correct Answer Incorrect Answer
    C 24 Correct Answer Incorrect Answer
    D 30 Correct Answer Incorrect Answer
    E none Correct Answer Incorrect Answer

    Solution

    First, find the prime factorization of 5040: 5040 ÷ 2 = 2520 2520 ÷ 2 = 1260 1260 ÷ 2 = 630 630 ÷ 2 = 315 315 ÷ 3 = 105 105 ÷ 3 = 35 35 ÷ 5 = 7 So, the prime factorization of 5040 is: 5040 = 2⁴ × 3² × 5 × 7. The formula for the number of divisors is: (Number of divisors) = (Exponent of 2 + 1)(Exponent of 3 + 1)(Exponent of 5 + 1)(Exponent of 7 + 1). Therefore, the number of divisors = (4 + 1)(2 + 1)(1 + 1)(1 + 1) = 5 × 3 × 2 × 2 = 60. Correct option: e

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