Write the prime factorization of 195. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).
Question
Write the prime factorization of 195. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).
Solution
Sure, let's find the prime factorization of 195.
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Start by dividing 195 by the smallest prime number, which is 2. Since 195 is not divisible by 2, we move to the next prime number, which is 3. 195 is not divisible by 3 either.
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The next prime number is 5. 195 divided by 5 equals 39. So, 5 is a prime factor of 195.
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Now, we need to find the prime factors of 39. 39 is not divisible by 2, 3, or 5.
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The next prime number is 7, but 39 is not divisible by 7.
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The next prime number is 11, but 39 is not divisible by 11.
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The next prime number is 13. 39 divided by 13 equals 3. So, 13 and 3 are prime factors of 39.
Therefore, the prime factorization of 195 is 3 * 5 * 13.
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