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Let $m$ be a positive integer such that $m$ has exactly $12$ positive divisors.  How many distinct prime factors does $m$ have?

 Jun 23, 2024

Best Answer 

 #1
avatar+85 
+1

to get the total number of divisors a number has you take the powers of the prime factors and add one then multiply. to give an example 20 is 2^2*5^1 so the total number of divisors is (2+1)(1+1) or 6. m has 12 divisors so we need to reverse this process. so 12 is 4*3 or 2*2*3. so the final answer is \(\boxed{2\space or \space 3}\)

 Jun 23, 2024
 #1
avatar+85 
+1
Best Answer

to get the total number of divisors a number has you take the powers of the prime factors and add one then multiply. to give an example 20 is 2^2*5^1 so the total number of divisors is (2+1)(1+1) or 6. m has 12 divisors so we need to reverse this process. so 12 is 4*3 or 2*2*3. so the final answer is \(\boxed{2\space or \space 3}\)

shmewy Jun 23, 2024

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