Question 828503: I am a number between 20 and 30, I am not divisible by 6 and the sum of my factor is 31, what number am I?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! I interpret "the sum of my factor is 31" as meaning that the sum of all the factors of the number is 31. (If you were allowed to choose just some of the factors and add them you would have more than one possible answer).
All the factors of 25 are 1, 5, and 25.
Their sum is 1+5+25=31.
I would say the solution is  .
The prime numbers between 20 and 30 are 23 and 29, and have sums of factor that are too low, because the only factors are 1 and the number.
Numbers that are not prime have more than two factors, but just the number itself plus 1 add up to at least 21. With just one more factor, there is a better chance for the sum to be 31 or less, but the only numbers with just 3 factors are prime numbers squared, and  is the only prime number square between 20 and 30.
The other numbers between 20 and 30 have 4 or more factors and the sum of factor ends up being too high. Just the number itself plus 1 add up to at least 21, and the smallest sum of 2 other factors would be 4+5=9, which would make the total sum
over 31 if the number is 22 or more (1+22+9=32).
The factors of 20 are 1,2,4,5,10, and 20, and add up to 42.
The factors of 21 are 1, 3, 7, and 21, and add up to 32.
I am confused by the phrase "I am not divisible by 6".
It does not seem necessary.
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