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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
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