Subjects algebra

Factors 30 069A32

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1. **State the problem:** We need to find how many factors the number 30 has. 2. **Recall the formula:** To find the number of factors of a number, first find its prime factorization. If the prime factorization of a number $n$ is $$n = p_1^{a_1} \times p_2^{a_2} \times \cdots \times p_k^{a_k},$$ then the number of factors is given by $$ (a_1 + 1)(a_2 + 1) \cdots (a_k + 1).$$ 3. **Find the prime factorization of 30:** $$30 = 2^1 \times 3^1 \times 5^1.$$ 4. **Apply the formula:** $$ (1 + 1)(1 + 1)(1 + 1) = 2 \times 2 \times 2 = 8.$$ 5. **Conclusion:** The number 30 has 8 factors in total. **Final answer:** 8