Subjects arithmetic

Divisors Division 874696

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1. **State the problem:** Find the result when 720 is divided by the number of its divisors. 2. **Formula and rules:** To solve this, we first find the number of divisors of 720. If the prime factorization of a number is $$n = p_1^{a_1} p_2^{a_2} \cdots p_k^{a_k}$$, then the number of divisors is given by $$ (a_1 + 1)(a_2 + 1) \cdots (a_k + 1) $$. 3. **Prime factorization of 720:** $$ 720 = 2^4 \times 3^2 \times 5^1 $$ 4. **Number of divisors:** $$ (4 + 1)(2 + 1)(1 + 1) = 5 \times 3 \times 2 = 30 $$ 5. **Divide 720 by the number of divisors:** $$ \frac{720}{30} $$ 6. **Simplify the fraction:** $$ \frac{\cancel{720}}{\cancel{30}} = 24 $$ 7. **Final answer:** The result is **24**. **Answer: C. 24**