SOLUTION: I am thinking of a three digit number. It is an odd multiple of three,and the product of its digits is 24. Its is larger that 225. What are all the numbers I could be thinking of?

Question 394328: I am thinking of a three digit number. It is an odd multiple of three,and the product of its digits is 24. Its is larger that 225. What are all the numbers I could be thinking of?

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Since the number is an odd multiple of 3, it must be an odd number. That is because an odd multiple of 3 cannot have a factor of 2.

List the possible all single digit factorizations of 24:

8 X 3 X 1
6 X 4 X 1
6 X 2 X 2
4 X 3 X 2

We can exclude 6 X 2 X 2 because it does not contain an odd digit hence you cannot form an odd 3 digit number.

We can exclude 6 X 4 X 1 because 6 + 4 + 1 is not divisible by 3, hence no three digit number formed from those digits will be divisible by 3.

8, 3, and 1 can be arranged in 6 different orders:

831, 813, 381, 318, 183, 138.

Exclude 318 because it is even and exclude 183 and 138 because they are less than 225.

So, 831, 813, and 381 are all possible.

4,3, and 2 can be arranged in 6 different ways (finding the ways is left as an exercise for the student. All of the 6 ways will be larger than 225, but only two of the ways are odd numbers.

All together you have 5 different possibilities.

John

My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

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