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42 and 48

2 x 3 x 7 = 42

24 x 3 = 48

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Q: Which numbers between 40 and 49 have 2 and 3 in their prime factorization use exponents to write the prime factorization of each number?
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Will prime factorization help find the number of factors of any number?

Write the prime factorization with exponents. Add 1 to each exponent. (Numbers without exponents actually have the exponent 1.) Multiply them together. That will be the number of factors.


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Can you predict the number of factors of any number by writing the prime factorization using exponents then adding one to the exponent and then finding the products of these numbers?

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