SOLUTION: Can anyone please help me? There is a number that has 2,5, and 8 as divisors. This number has exactly seven additional divisors. What is the number? Thank you for your help:)

SOLUTION: Can anyone please help me? There is a number that has 2,5, and 8 as divisors. This number has exactly seven additional divisors. What is the number? Thank you for your help:)

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Question 327163: Can anyone please help me?
There is a number that has 2,5, and 8 as divisors. This number has exactly seven additional divisors. What is the number?
Thank you for your help:)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

There is more than one answer to this problem. In fact, there are an infinite number of answers.

Start with 5 times 8 equals 40. All of the divisors of 40 are:

1, 2, 4, 5, 8, 10, 20, and 40, for a total of 8 divisors. But the number we seek has exactly 10 total divisors. Hence you can select any prime number other than 2 and 5 which we will call

and multiply this number times 40. Now we will have a number we can call

which has exactly 10 divisors, to wit: 1, 2, 4, 5, 8, 10, 20, 40,

, and

.

For example: Let

. Then

. The prime factorization of

is

.

Or let

. Then

, the prime factorization of which is

And so on.

John

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