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Dear Math Central,
I am a 7th grade student and having trouble figuring this problem out? Please help if you can, becoming frustrated.

Thanks,
Grace

THREE DIGIT NUMBER

What three digit positive integer is exactly 32 times the sum of its digits?
 

 

Hi Grace,

The sum of the digits is one of the numbers 3, 4, ..., 27. These are the 25 possibilities to try: You multiply this sum by 32, and if you get back a three-digit number whose digits add up to the number you started with, then Bingo!, you found it:

3 x 32 = 96, not a 3-digit number
4 x 32 = 128, 1+2+8 = 11, not 4
5 x 32 = 160, 1+6+0 = 7, not 5
...

Claude 		 
 

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