SOLUTION: When 270 is divided by the odd number n, the quotient is a positive prime number and the remainder is zero. What is n?

Question 256389: When 270 is divided by the odd number n, the quotient is a positive prime number
and the remainder is zero. What is n?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

First look at the prime factorization of 270. The quick way is to realize that you have 27 times 10 or 3 times 3 times 3 times 5 times 2.

If you are going to divide 270 by something and get a positive prime number, then that positive prime number must be one of the above prime numbers, namely 2, 3, or 5. Furthermore, the 'something' must be the product of all of the prime factors except for the one that is the desired quotient. In order for n to be odd, it cannot have 2 as a factor. Therefore, the quotient must be 2 and n must be the product of 27 times 5 = 135.

John

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