Subjects algebra

Factors 30

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1. The problem is to find how many factors the number 30 has. 2. To find the number of factors of a number, we first find its prime factorization. 3. The prime factorization of 30 is $$30 = 2^1 \times 3^1 \times 5^1$$. 4. The formula to find the number of factors from prime factorization $$n = p_1^{a_1} \times p_2^{a_2} \times \cdots \times p_k^{a_k}$$ is $$(a_1 + 1)(a_2 + 1) \cdots (a_k + 1)$$. 5. Applying this formula to 30, we get $$(1+1)(1+1)(1+1) = 2 \times 2 \times 2 = 8$$. 6. Therefore, 30 has 8 factors in total.